Single Best Answer MCQs for Sub-Topics of Topic 4: Geometry

Question 1. Which of the following best describes a point in geometry?

(A) A shape with defined length and width

(B) A location with no dimension

(C) A line segment

(D) A curve

Question 2. How many lines can pass through a single given point?

(A) One

(B) Two

(C) A finite number

(D) An infinite number

Question 3. A set of points extending infinitely in both directions with no thickness is called a:

(A) Ray

(B) Line segment

(C) Line

(D) Plane

Question 4. Two distinct lines in a plane can either be parallel or:

(A) Skew

(B) Intersecting

(C) Coincident

(D) Perpendicular (Perpendicular lines are a type of intersecting lines)

Question 5. A flat surface that extends infinitely in all directions is known as a:

(A) Line

(B) Plane

(C) Space

(D) Region

Question 6. What is the minimum number of points required to uniquely determine a line?

(A) One

(B) Two

(C) Three

(D) Four

Question 7. A part of a line with two endpoints is called a:

(A) Ray

(B) Line

(C) Line segment

(D) Point

Question 8. A part of a line with one endpoint and extending infinitely in one direction is called a:

(A) Line segment

(B) Ray

(C) Line

(D) Angle

Question 9. Which of the following is an example of a pair of intersecting lines?

(A) Railway tracks

(B) Adjacent edges of a book

(C) Opposite edges of a ruler

(D) Lines on a ruled paper

Question 10. How many dimensions does a plane have?

(A) One

(B) Two

(C) Three

(D) Zero

Question 11. A curve that starts and ends at the same point is called a:

(A) Open curve

(B) Line segment

(C) Closed curve

(D) Ray

Question 12. Which of the following can be drawn on a flat piece of paper representing a plane?

(A) Point, line, plane

(B) Point, line segment, ray

(C) Plane, space

(D) Line, space

Question 13. If two lines intersect, they meet at exactly:

(A) One point

(B) Two points

(C) An infinite number of points

(D) No point

Question 14. Parallel lines are lines in the same plane that:

(A) Intersect at a single point

(B) Never intersect

(C) Intersect at multiple points

(D) Coincide

Question 15. The surface of a table is a good model for a small portion of a:

(A) Line

(B) Ray

(C) Plane

(D) Line segment

Question 16. A line segment PQ is denoted as:

(A) $\overleftrightarrow{PQ}$

(B) $\overrightarrow{PQ}$

(C) $\overline{PQ}$

(D) $PQ$ (lowercase)

Question 17. A ray AB (starting at A and going through B) is denoted as:

(A) $\overleftrightarrow{AB}$

(B) $\overrightarrow{AB}$

(C) $\overline{AB}$

(D) $AB$ (lowercase)

Question 18. Which of the following represents a closed curve?

(A) A straight line

(B) A circle

(C) A V-shape

(D) A zig-zag line that does not meet its starting point

Question 19. Consider three distinct points A, B, and C. If A, B, and C lie on the same line, they are called:

(A) Non-collinear points

(B) Collinear points

(C) Coplanar points

(D) Vertex points

Question 20. How many planes can pass through three non-collinear points?

(A) Zero

(B) One

(C) Two

(D) An infinite number

Question 21. How many endpoints does a line segment have?

(A) Zero

(B) One

(C) Two

(D) Infinite

Question 22. Which of the following is a basic undefined term in geometry?

(A) Angle

(B) Triangle

(C) Point

(D) Square

Question 1. The standard unit for measuring the length of a line segment in the SI system is:

(A) Inch

(B) Foot

(C) Metre

(D) Centimetre

Question 2. Which instrument is typically used to measure the length of a line segment?

(A) Protractor

(B) Compass

(C) Ruler or measuring tape

(D) Set square

Question 3. When comparing two line segments, we compare their:

(A) Direction

(B) Position

(C) Colour

(D) Length

Question 4. An angle is formed by two rays originating from the same point. This common point is called the:

(A) Arm

(B) Vertex

(C) Degree

(D) Arc

Question 5. The two rays forming an angle are called the:

(A) Vertices

(B) Sides or arms

(C) Degrees

(D) Arcs

Question 6. The region between the two arms of an angle is called the:

(A) Exterior

(B) Interior

(C) Vertex

(D) Boundary

Question 7. A point that lies outside the angle is in its:

(A) Interior

(B) Vertex

(C) Exterior

(D) Arm

Question 8. The standard unit for measuring angles is:

(A) Metre

(B) Degree ($\circ$)

(C) Kilogram

(D) Second

Question 9. Which instrument is commonly used to measure angles?

(A) Ruler

(B) Compass

(C) Protractor

(D) Divider

Question 10. What is the measure of a straight angle?

(A) $0^\circ$

(B) $90^\circ$

(C) $180^\circ$

(D) $360^\circ$

Question 11. A complete angle measures:

(A) $90^\circ$

(B) $180^\circ$

(C) $270^\circ$

(D) $360^\circ$

Question 12. If we measure a line segment using a scale where the initial point is at 2 cm mark and the endpoint is at 7.5 cm mark, what is the length of the segment?

(A) 2 cm

(B) 7.5 cm

(C) 5.5 cm

(D) 9.5 cm

Question 13. The vertex of $\angle \text{XYZ}$ is:

(A) Point X

(B) Point Y

(C) Point Z

(D) The angle itself

Question 14. The arms of $\angle \text{PQR}$ are:

(A) $\overrightarrow{PQ}$ and $\overrightarrow{QR}$

(B) $\overline{PQ}$ and $\overline{QR}$

(C) $\overrightarrow{QP}$ and $\overrightarrow{QR}$

(D) Points P and R

Question 15. What is the measure of a zero angle?

(A) $0^\circ$

(B) $90^\circ$

(C) $180^\circ$

(D) $360^\circ$

Question 16. If a ray starts from point A and passes through point B, and another ray starts from A and passes through point C, they form an angle with vertex A, provided A, B, and C are:

(A) Collinear

(B) Non-collinear

(C) Coplanar

(D) Identical

Question 17. A point R is in the interior of $\angle \text{PQR}$. Which of the following is true?

(A) R is on the vertex Q.

(B) R is on either ray QP or QR.

(C) R is between the rays QP and QR.

(D) R is outside the angle.

Question 18. The angle formed by the hands of a clock at 3 o'clock is related to which type of angle measurement?

(A) Straight angle

(B) Reflex angle

(C) Right angle

(D) Complete angle

Question 19. To accurately measure a line segment using a ruler, one end of the segment should be placed at the _____ mark.

(A) Any convenient mark

(B) The 1 cm mark

(C) The zero mark

(D) The 10 cm mark

Question 20. The measure of an angle is independent of the:

(A) Length of its arms

(B) Opening between its arms

(C) Vertex position

(D) Unit of measurement

Question 1. An angle measuring more than $0^\circ$ and less than $90^\circ$ is called a(n):

(A) Right angle

(B) Obtuse angle

(C) Acute angle

(D) Straight angle

Question 2. An angle measuring exactly $90^\circ$ is called a(n):

(A) Acute angle

(B) Obtuse angle

(C) Right angle

(D) Reflex angle

Question 3. An angle measuring more than $90^\circ$ but less than $180^\circ$ is called a(n):

(A) Straight angle

(B) Obtuse angle

(C) Acute angle

(D) Reflex angle

Question 4. An angle measuring exactly $180^\circ$ is called a(n):

(A) Right angle

(B) Complete angle

(C) Straight angle

(D) Zero angle

Question 5. An angle measuring more than $180^\circ$ but less than $360^\circ$ is called a(n):

(A) Acute angle

(B) Obtuse angle

(C) Reflex angle

(D) Straight angle

Question 6. When two lines intersect such that they form a right angle at the point of intersection, they are called:

(A) Parallel lines

(B) Intersecting lines

(C) Skew lines

(D) Perpendicular lines

Question 7. The symbol $\perp$ is used to denote:

(A) Parallelism

(B) Congruence

(C) Perpendicularity

(D) Similarity

Question 8. A line that is perpendicular to a line segment at its midpoint is called a:

(A) Median

(B) Altitude

(C) Angle bisector

(D) Perpendicular bisector

Question 9. If line $m \perp$ line $n$, then the angle between them is:

(A) $0^\circ$

(B) $90^\circ$

(C) $180^\circ$

(D) $360^\circ$

Question 10. The reflection of an object across a line is related to:

(A) Parallel lines

(B) Skew lines

(C) Perpendicular lines

(D) Transversals

Question 11. Which type of angle is formed by the corner of a square table?

(A) Acute angle

(B) Obtuse angle

(C) Right angle

(D) Straight angle

Question 12. The angle formed by the hour hand and minute hand of a clock at 6 o'clock is a:

(A) Right angle

(B) Acute angle

(C) Obtuse angle

(D) Straight angle

Question 13. A zero angle represents:

(A) No rotation

(B) Half rotation

(C) Quarter rotation

(D) Full rotation

Question 14. A complete angle represents:

(A) No rotation

(B) Half rotation

(C) Quarter rotation

(D) Full rotation

Question 15. If a line $p$ is the perpendicular bisector of line segment $AB$, then:

(A) $p$ is parallel to $AB$

(B) $p$ intersects $AB$ at any point

(C) $p$ intersects $AB$ at its midpoint and is perpendicular to $AB$

(D) $p$ is parallel to the perpendicular to $AB$

Question 16. Which of the following is NOT a type of angle?

(A) Linear angle

(B) Acute angle

(C) Reflex angle

(D) Obtuse angle

Question 17. If $\angle A = 45^\circ$, then $\angle A$ is a(n):

(A) Right angle

(B) Obtuse angle

(C) Acute angle

(D) Straight angle

Question 18. If $\angle B = 110^\circ$, then $\angle B$ is a(n):

(A) Acute angle

(B) Obtuse angle

(C) Reflex angle

(D) Straight angle

Question 19. If two segments $\overline{AB}$ and $\overline{CD}$ are perpendicular, it means the lines containing them:

(A) Are parallel

(B) Intersect at $0^\circ$

(C) Intersect at $90^\circ$

(D) Do not intersect

Question 20. A road sign shaped like a diamond (rhombus) has angles that are either acute or:

(A) Right

(B) Straight

(C) Obtuse

(D) Reflex

Question 21. The sum of the angles around a point is:

(A) $90^\circ$

(B) $180^\circ$

(C) $270^\circ$

(D) $360^\circ$

Question 1. Two angles are complementary if their sum is:

(A) $90^\circ$

(B) $180^\circ$

(C) $270^\circ$

(D) $360^\circ$

Question 2. Two angles are supplementary if their sum is:

(A) $90^\circ$

(B) $180^\circ$

(C) $270^\circ$

(D) $360^\circ$

Question 3. The complement of an angle of $55^\circ$ is:

(A) $35^\circ$

(B) $45^\circ$

(C) $125^\circ$

(D) $180^\circ$

Question 4. The supplement of an angle of $70^\circ$ is:

(A) $20^\circ$

(B) $90^\circ$

(C) $110^\circ$

(D) $180^\circ$

Question 5. Two angles are adjacent if they have a common vertex and a common arm, and their non-common arms are on different sides of the common arm. Which condition is NOT necessary for two angles to be adjacent?

(A) Common vertex

(B) Common arm

(C) Non-common arms on opposite sides of the common arm

(D) Their sum is $90^\circ$ or $180^\circ$

Question 6. A linear pair of angles is a pair of adjacent angles whose non-common arms form a:

(A) Right angle

(B) Straight line

(C) Reflex angle

(D) Point

Question 7. The sum of the angles in a linear pair is always:

(A) $90^\circ$

(B) $180^\circ$

(C) $270^\circ$

(D) $360^\circ$

Question 8. When two lines intersect, the angles opposite to each other at the intersection point are called:

(A) Adjacent angles

(B) Complementary angles

(C) Vertically opposite angles

(D) Linear pair

Question 9. Vertically opposite angles are always:

(A) Complementary

(B) Supplementary

(C) Equal

(D) Adjacent

Question 10. If two angles form a linear pair and one angle is $75^\circ$, what is the measure of the other angle?

(A) $15^\circ$

(B) $105^\circ$

(C) $180^\circ$

(D) $285^\circ$

Question 11. If $\angle A$ and $\angle B$ are complementary and $\angle A = 3x^\circ$ and $\angle B = 2x^\circ$, what is the value of $x$?

(A) 18

(B) 30

(C) 45

(D) 90

Question 12. If two angles form a linear pair and one angle is half the other, what are the measures of the two angles?

(A) $60^\circ, 120^\circ$

(B) $30^\circ, 60^\circ$

(C) $45^\circ, 90^\circ$

(D) $90^\circ, 90^\circ$

Question 13. Two lines AB and CD intersect at O. If $\angle AOC = 50^\circ$, find the measure of $\angle BOD$.

(A) $40^\circ$

(B) $50^\circ$

(C) $130^\circ$

(D) $180^\circ$

Question 14. Two lines AB and CD intersect at O. If $\angle AOC = 50^\circ$, find the measure of $\angle AOD$.

(A) $40^\circ$

(B) $50^\circ$

(C) $130^\circ$

(D) $180^\circ$

Question 15. If $\angle P$ and $\angle Q$ are supplementary angles and $\angle P = 2\angle Q$, find the measures of $\angle P$ and $\angle Q$.

(A) $\angle P = 60^\circ, \angle Q = 120^\circ$

(B) $\angle P = 120^\circ, \angle Q = 60^\circ$

(C) $\angle P = 90^\circ, \angle Q = 90^\circ$

(D) $\angle P = 30^\circ, \angle Q = 150^\circ$

Question 16. Which pair of angles always sums to $180^\circ$?

(A) Complementary angles

(B) Vertically opposite angles

(C) Adjacent angles

(D) Supplementary angles

Question 17. If two adjacent angles are supplementary, they form a:

(A) Right angle

(B) Acute angle

(C) Linear pair

(D) Reflex angle

Question 18. Two angles are adjacent and form an angle of $90^\circ$. They are:

(A) Complementary

(B) Supplementary

(C) Vertically opposite

(D) A linear pair

Question 19. If two angles are vertically opposite and one angle is $100^\circ$, the other angle is:

(A) $80^\circ$

(B) $100^\circ$

(C) $180^\circ$

(D) $200^\circ$

Question 20. Can two acute angles be supplementary?

(A) Yes, always

(B) Yes, if their sum is $180^\circ$

(C) No, because their sum is always less than $180^\circ$

(D) Only if they are both $90^\circ$

Question 21. Can two obtuse angles form a linear pair?

(A) Yes, always

(B) Yes, if their sum is $180^\circ$

(C) No, because their sum is always greater than $180^\circ$

(D) Only if they are both $90^\circ$

Question 22. If two angles are both supplementary and vertically opposite, what is the measure of each angle?

(A) $0^\circ$

(B) $90^\circ$

(C) $180^\circ$

(D) $360^\circ$

Question 23. If $\angle X = 25^\circ$, what type of angle is its complement?

(A) Acute angle

(B) Right angle

(C) Obtuse angle

(D) Straight angle

Question 24. If $\angle Y = 150^\circ$, what type of angle is its supplement?

(A) Acute angle

(B) Right angle

(C) Obtuse angle

(D) Reflex angle

Question 1. A line that intersects two or more lines at distinct points is called a:

(A) Parallel line

(B) Perpendicular line

(C) Transversal

(D) Ray

Question 2. When a transversal intersects two lines, it forms eight angles. Which pair of angles lies on opposite sides of the transversal and between the two lines?

(A) Corresponding angles

(B) Alternate interior angles

(C) Alternate exterior angles

(D) Consecutive interior angles

Question 3. When a transversal intersects two lines, which pair of angles are on the same side of the transversal and between the two lines?

(A) Corresponding angles

(B) Alternate interior angles

(C) Alternate exterior angles

(D) Consecutive interior angles (or Same-side interior angles)

Question 4. When a transversal intersects two lines, which pair of angles are on the same side of the transversal, with one inside and one outside the two lines?

(A) Corresponding angles

(B) Alternate interior angles

(C) Alternate exterior angles

(D) Vertically opposite angles

Question 5. If a transversal intersects two parallel lines, then each pair of corresponding angles is:

(A) Complementary

(B) Supplementary

(C) Equal

(D) Zero

Question 6. If a transversal intersects two parallel lines, then each pair of alternate interior angles is:

(A) Complementary

(B) Supplementary

(C) Equal

(D) Double of each other

Question 7. If a transversal intersects two parallel lines, then each pair of consecutive interior angles is:

(A) Equal

(B) Complementary

(C) Supplementary

(D) Reflex

Question 8. If a transversal intersects two lines such that a pair of corresponding angles are equal, then the two lines are:

(A) Perpendicular

(B) Intersecting

(C) Parallel

(D) Coincident

Question 9. If a transversal intersects two lines such that the sum of a pair of consecutive interior angles is $180^\circ$, then the two lines are:

(A) Perpendicular

(B) Intersecting

(C) Parallel

(D) Skew

Question 10. In the figure below (imagine a transversal intersecting two lines), if $\angle 1$ and $\angle 5$ are corresponding angles, and line $l ||$ line $m$, then:

(A) $\angle 1 = \angle 5$

(B) $\angle 1 + \angle 5 = 90^\circ$

(C) $\angle 1 + \angle 5 = 180^\circ$

(D) $\angle 1 > \angle 5$

Question 11. In the same figure as Question 10, if $\angle 3$ and $\angle 6$ are alternate interior angles, and line $l ||$ line $m$, then:

(A) $\angle 3 + \angle 6 = 90^\circ$

(B) $\angle 3 + \angle 6 = 180^\circ$

(C) $\angle 3 = \angle 6$

(D) $\angle 3 < \angle 6$

Question 12. In the same figure as Question 10, if $\angle 4$ and $\angle 6$ are consecutive interior angles, and line $l ||$ line $m$, then:

(A) $\angle 4 = \angle 6$

(B) $\angle 4 + \angle 6 = 90^\circ$

(C) $\angle 4 + \angle 6 = 180^\circ$

(D) $\angle 4 > \angle 6$

Question 13. If two lines are intersected by a transversal such that the alternate exterior angles are equal, then the lines are:

(A) Perpendicular

(B) Parallel

(C) Coincident

(D) Intersecting but not parallel

Question 14. Which of the following is NOT a criterion for two lines to be parallel when intersected by a transversal?

(A) Corresponding angles are equal.

(B) Alternate interior angles are equal.

(C) Consecutive interior angles are complementary.

(D) Consecutive interior angles are supplementary.

Question 15. If two parallel lines are intersected by a transversal, and one of the interior angles on the same side is $100^\circ$, what is the measure of the other interior angle on the same side?

(A) $80^\circ$

(B) $100^\circ$

(C) $180^\circ$

(D) $260^\circ$

Question 16. If a transversal intersects two lines such that a pair of alternate interior angles are $40^\circ$ and $50^\circ$, what can you say about the lines?

(A) They are parallel.

(B) They are perpendicular.

(C) They intersect but are not parallel.

(D) They are coincident.

Question 17. Consider lines $l$ and $m$ and a transversal $t$. If $\angle A$ and $\angle B$ are corresponding angles formed by $t$ intersecting $l$ and $m$. If $\angle A = (2x+10)^\circ$ and $\angle B = (3x-20)^\circ$. If $l || m$, what is the value of $x$?

(A) 10

(B) 20

(C) 30

(D) 40

Question 18. When two parallel lines are cut by a transversal, the sum of consecutive exterior angles on the same side of the transversal is:

(A) $90^\circ$

(B) $180^\circ$

(C) $270^\circ$

(D) $360^\circ$

Question 19. If two lines are parallel, any transversal will create alternate interior angles that are:

(A) Supplementary

(B) Unequal

(C) Equal

(D) Complementary

Question 20. A transversal intersects three distinct lines. How many points of intersection are there at minimum?

(A) 1

(B) 2

(C) 3

(D) 6

Question 21. If lines $p$ and $q$ are parallel, and line $r$ is perpendicular to line $p$, then line $r$ must also be _____ to line $q$.

(A) Parallel

(B) Perpendicular

(C) Skew

(D) Coincident

Question 1. Euclidean geometry is primarily based on a system of definitions, axioms, postulates, and:

(A) Opinions

(B) Conjectures

(C) Theorems

(D) Experiments

Question 2. Which of the following is considered an undefined term in Euclidean geometry?

(A) Triangle

(B) Circle

(C) Line

(D) Area

Question 3. Statements that are assumed to be true without proof are called:

(A) Theorems

(B) Definitions

(C) Propositions

(D) Axioms or Postulates

Question 4. Statements that are proven true using definitions, axioms, postulates, and previously proven theorems are called:

(A) Conjectures

(B) Axioms

(C) Definitions

(D) Theorems

Question 5. Euclid's Elements is a foundational work in geometry. It primarily deals with geometry in:

(A) Curved space

(B) A plane (2D)

(C) Hyperbolic space

(D) 4 dimensions

Question 6. According to Euclid's Postulate 1, a straight line can be drawn from:

(A) Any point to any other point

(B) Only between two specified points

(C) Only through the origin

(D) Through infinite points

Question 7. Euclid's Postulate 2 states that a terminated line (line segment) can be produced indefinitely in a straight line. This means:

(A) A line segment has infinite length

(B) A line segment can be extended to form a line

(C) A line has a finite length

(D) A ray can be extended in both directions

Question 8. Euclid's Postulate 3 states that a circle can be described with any centre and any radius. This postulate:

(A) Limits the number of possible circles

(B) Guarantees the existence of circles of all sizes

(C) Defines a tangent to a circle

(D) Relates circles to lines

Question 9. Euclid's Postulate 4 states that all right angles are equal to one another. This implies that the measure of a right angle is a fixed value, specifically:

(A) $45^\circ$

(B) $90^\circ$

(C) $180^\circ$

(D) $360^\circ$

Question 10. Euclid's Fifth Postulate, also known as the Parallel Postulate, is the most famous and historically significant. Which of the following is NOT an equivalent statement to Euclid's Fifth Postulate?

(A) Playfair's Axiom: Through a point not on a given line, exactly one line can be drawn parallel to the given line.

(B) The sum of the angles in a triangle is $180^\circ$.

(C) If two lines are parallel to the same line, they are parallel to each other.

(D) Two distinct lines are either parallel or they intersect at exactly one point.

Question 11. Which of the following is a key characteristic of an axiom or postulate?

(A) It must be proven rigorously.

(B) It is a statement that is assumed to be true.

(C) It is derived from other known facts.

(D) It is a mere observation without any basis.

Question 12. The concept of a proof in Euclidean geometry involves starting from axioms, postulates, definitions, and previously proven theorems to logically deduce the truth of a:

(A) Definition

(B) Postulate

(C) Theorem

(D) Undefined term

Question 13. If two distinct points P and Q are given, how many straight lines can be drawn that pass through both P and Q?

(A) Zero

(B) Exactly one

(C) Two

(D) An infinite number

Question 14. The phrase "Things which are equal to the same thing are equal to one another" is an example of Euclid's:

(A) Definition

(B) Postulate

(C) Axiom (Common Notion)

(D) Theorem

Question 15. "If equals be added to equals, the wholes are equal." This is another example of Euclid's:

(A) Definition

(B) Postulate

(C) Axiom (Common Notion)

(D) Theorem

Question 16. Non-Euclidean geometries (like spherical or hyperbolic geometry) were developed by questioning or replacing:

(A) All of Euclid's postulates

(B) Only Euclid's Fifth Postulate

(C) Only Euclid's first four postulates

(D) All of Euclid's axioms

Question 17. In the context of Euclidean geometry, a "plane" is typically visualized as a flat surface extending infinitely. This concept is introduced as a(n):

(A) Defined term

(B) Undefined term

(C) Theorem

(D) Lemma

Question 18. According to a common axiom (or postulate), if two distinct lines intersect, how many points do they have in common?

(A) Zero

(B) Exactly one

(C) Two

(D) An infinite number

Question 19. A theorem is a statement that has been proven true. The process of proving a theorem relies on:

(A) Intuition and estimation

(B) Measurement and observation

(C) Logical deduction

(D) Majority consensus

Question 20. Which of the following is a definition in Euclidean geometry?

(A) A point is that which has no part.

(B) A line is a breadthless length.

(C) A straight line is one which lies evenly with the points on itself.

(D) All of the above are definitions from Euclid's Elements.

Question 21. The system of Euclidean geometry built upon Euclid's postulates describes space as being:

(A) Curved

(B) Flat

(C) Finite

(D) Non-uniform

Question 1. A simple closed curve made up of only line segments is called a:

(A) Circle

(B) Polygon

(C) Curve

(D) Ray

Question 2. The line segments forming a polygon are called its:

(A) Diagonals

(B) Vertices

(C) Sides

(D) Angles

Question 3. The endpoints of the sides of a polygon are called its:

(A) Sides

(B) Diagonals

(C) Vertices

(D) Edges

Question 4. A line segment connecting two non-adjacent vertices of a polygon is called a:

(A) Side

(B) Edge

(C) Diagonal

(D) Altitude

Question 5. A polygon with 3 sides is called a:

(A) Quadrilateral

(B) Pentagon

(C) Triangle

(D) Hexagon

Question 6. A polygon with 4 sides is called a:

(A) Triangle

(B) Pentagon

(C) Quadrilateral

(D) Hexagon

Question 7. A polygon whose interior angles are all less than $180^\circ$ is called a:

(A) Concave polygon

(B) Regular polygon

(C) Convex polygon

(D) Irregular polygon

Question 8. A polygon in which at least one interior angle is greater than $180^\circ$ is called a:

(A) Convex polygon

(B) Regular polygon

(C) Concave polygon

(D) Equilateral polygon

Question 9. A polygon that is both equiangular (all angles equal) and equilateral (all sides equal) is called a:

(A) Concave polygon

(B) Regular polygon

(C) Irregular polygon

(D) Complex polygon

Question 10. A polygon that is NOT regular is called a(n):

(A) Convex polygon

(B) Concave polygon

(C) Irregular polygon

(D) Complex polygon

Question 11. What is the minimum number of sides a polygon can have?

(A) 1

(B) 2

(C) 3

(D) 4

Question 12. A polygon with 5 sides is called a:

(A) Quadrilateral

(B) Hexagon

(C) Octagon

(D) Pentagon

Question 13. A polygon with 6 sides is called a:

(A) Pentagon

(B) Hexagon

(C) Heptagon

(D) Octagon

Question 14. The sum of the exterior angles of any convex polygon is always:

(A) $90^\circ$

(B) $180^\circ$

(C) $360^\circ$

(D) Depends on the number of sides

Question 15. In a regular polygon with $n$ sides, the measure of each interior angle is given by the formula:

(A) $\frac{(n-2) \times 180^\circ}{n}$

(B) $\frac{360^\circ}{n}$

(C) $(n-2) \times 180^\circ$

(D) $(n-2) \times 90^\circ$

Question 16. In a regular polygon with $n$ sides, the measure of each exterior angle is given by the formula:

(A) $\frac{(n-2) \times 180^\circ}{n}$

(B) $\frac{360^\circ}{n}$

(C) $(n-2) \times 180^\circ$

(D) $(n-2) \times 90^\circ$

Question 17. The number of diagonals in a polygon with $n$ sides is given by the formula:

(A) $n(n-1)/2$

(B) $n(n-2)/2$

(C) $n(n-3)/2$

(D) $n(n+1)/2$

Question 18. How many diagonals does a pentagon have?

(A) 2

(B) 3

(C) 4

(D) 5

Question 19. A polygon where some part of a diagonal lies outside the polygon is a:

(A) Convex polygon

(B) Concave polygon

(C) Regular polygon

(D) Equilateral polygon

Question 20. Which of the following is an example of a regular polygon?

(A) An isosceles triangle

(B) A rectangle

(C) A rhombus

(D) A square

Question 21. A figure formed by three non-collinear points joined by line segments is a:

(A) Quadrilateral

(B) Triangle

(C) Pentagon

(D) Circle

Question 22. In any polygon, the number of vertices is equal to the number of:

(A) Diagonals

(B) Sides

(C) Triangles formed by diagonals from one vertex

(D) Reflex angles

Question 1. A triangle is a polygon with:

(A) 2 sides

(B) 3 sides

(C) 4 sides

(D) 5 sides

Question 2. The three line segments forming a triangle are called its:

(A) Vertices

(B) Angles

(C) Sides

(D) Diagonals

Question 3. The three points where the sides of a triangle meet are called its:

(A) Sides

(B) Angles

(C) Vertices

(D) Midpoints

Question 4. A triangle with all three sides of different lengths is called a:

(A) Isosceles triangle

(B) Equilateral triangle

(C) Scalene triangle

(D) Right-angled triangle

Question 5. A triangle with exactly two sides of equal length is called a:

(A) Scalene triangle

(B) Equilateral triangle

(C) Isosceles triangle

(D) Acute-angled triangle

Question 6. A triangle with all three sides of equal length is called a:

(A) Isosceles triangle

(B) Equilateral triangle

(C) Scalene triangle

(D) Obtuse-angled triangle

Question 7. A triangle in which all three angles are acute (less than $90^\circ$) is called a(n):

(A) Right-angled triangle

(B) Obtuse-angled triangle

(C) Acute-angled triangle

(D) Equiangular triangle

Question 8. A triangle in which one angle is obtuse (greater than $90^\circ$) is called a(n):

(A) Right-angled triangle

(B) Obtuse-angled triangle

(C) Acute-angled triangle

(D) Isosceles triangle

Question 9. A triangle in which one angle is a right angle (exactly $90^\circ$) is called a(n):

(A) Acute-angled triangle

(B) Obtuse-angled triangle

(C) Right-angled triangle

(D) Equilateral triangle

Question 10. An equilateral triangle is also equiangular. What is the measure of each angle in an equilateral triangle?

(A) $30^\circ$

(B) $45^\circ$

(C) $60^\circ$

(D) $90^\circ$

Question 11. Can a triangle have two obtuse angles?

(A) Yes, always

(B) Yes, if they are less than $100^\circ$

(C) No, because the sum of two obtuse angles is greater than $180^\circ$

(D) Only if the third angle is $0^\circ$

Question 12. Can a triangle have two right angles?

(A) Yes, always

(B) Yes, if the third angle is acute

(C) No, because the sum of two right angles is $180^\circ$ and the third angle must be greater than $0^\circ$

(D) Yes, in non-Euclidean geometry

Question 13. A triangle is a convex polygon. True or False?

(A) True

(B) False

(C) Cannot be determined

(D) Only if it is equilateral

Question 14. In a triangle, the number of vertices is equal to the number of:

(A) Diagonals

(B) Sides and angles

(C) Only sides

(D) Only angles

Question 15. Can a scalene triangle be isosceles?

(A) Yes, always

(B) Yes, sometimes

(C) No

(D) Only if it is equilateral

Question 16. Can an isosceles triangle be equilateral?

(A) Yes, always

(B) Yes, sometimes (specifically, when all three sides are equal)

(C) No

(D) Only if its angles are $90^\circ, 45^\circ, 45^\circ$

Question 17. A triangle with angles $30^\circ, 60^\circ, 90^\circ$ is classified as:

(A) Acute-angled and isosceles

(B) Right-angled and scalene

(C) Obtuse-angled and equilateral

(D) Right-angled and isosceles

Question 18. A triangle with sides 5 cm, 5 cm, and 7 cm is classified as:

(A) Scalene triangle

(B) Equilateral triangle

(C) Isosceles triangle

(D) Right-angled triangle

Question 19. The region enclosed by the sides of a triangle is called the:

(A) Exterior

(B) Boundary

(C) Interior

(D) Vertex

Question 20. A triangle divides the plane into how many regions?

(A) 1

(B) 2

(C) 3

(D) Infinite

Question 21. Which of the following cannot be the angles of a triangle?

(A) $50^\circ, 60^\circ, 70^\circ$

(B) $90^\circ, 45^\circ, 45^\circ$

(C) $30^\circ, 30^\circ, 120^\circ$

(D) $60^\circ, 60^\circ, 61^\circ$

Question 1. The sum of the interior angles of any triangle is always:

(A) $90^\circ$

(B) $180^\circ$

(C) $270^\circ$

(D) $360^\circ$

Question 2. If two angles of a triangle are $40^\circ$ and $60^\circ$, what is the measure of the third angle?

(A) $40^\circ$

(B) $60^\circ$

(C) $80^\circ$

(D) $100^\circ$

Question 3. The exterior angle of a triangle is equal to the sum of the two:

(A) Adjacent interior angles

(B) Opposite interior angles

(C) All three interior angles

(D) Exterior angles

Question 4. In triangle ABC, if the exterior angle at vertex C is $110^\circ$ and $\angle A = 50^\circ$, find $\angle B$.

(A) $40^\circ$

(B) $60^\circ$

(C) $70^\circ$

(D) $110^\circ$

Question 5. In an isosceles triangle, the angles opposite to the equal sides are:

(A) Complementary

(B) Supplementary

(C) Equal

(D) Different

Question 6. In $\triangle$ABC, if AB = AC, then which angles are equal?

(A) $\angle A = \angle B$

(B) $\angle A = \angle C$

(C) $\angle B = \angle C$

(D) All angles are equal

Question 7. The converse of the Isosceles Triangle Theorem states that if two angles of a triangle are equal, then the sides opposite to them are:

(A) Different

(B) Parallel

(C) Equal

(D) Perpendicular

Question 8. Which of the following represents the Triangle Inequality Theorem?

(A) The square of the longest side is equal to the sum of the squares of the other two sides.

(B) The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

(C) The difference of the lengths of any two sides is equal to the third side.

(D) All angles sum to $180^\circ$.

Question 9. The side opposite the largest angle in a triangle is always the:

(A) Smallest side

(B) Medium side

(C) Largest side

(D) Equal to the smallest side

Question 10. In $\triangle$PQR, if $\angle Q > \angle R$, then which inequality concerning side lengths must be true?

(A) PQ > PR

(B) PQ < PR

(C) QR > PR

(D) QR < PQ

Question 11. Can a triangle be formed with side lengths 3 cm, 4 cm, and 8 cm?

(A) Yes

(B) No

(C) Only if it is a right triangle

(D) Only if it is an isosceles triangle

Question 12. In a triangle, if one angle is $90^\circ$, the other two angles must be:

(A) Obtuse

(B) Right

(C) Acute

(D) Supplementary

Question 13. If the angles of a triangle are in the ratio $1:2:3$, what are the measures of the angles?

(A) $30^\circ, 60^\circ, 90^\circ$

(B) $20^\circ, 40^\circ, 60^\circ$

(C) $45^\circ, 45^\circ, 90^\circ$

(D) $60^\circ, 60^\circ, 60^\circ$

Question 14. The difference between the lengths of any two sides of a triangle is _____ than the length of the third side.

(A) Greater than

(B) Less than

(C) Equal to

(D) Greater than or equal to

Question 15. In triangle XYZ, if XY = 8 cm, YZ = 15 cm, and XZ = 17 cm, which angle is the largest?

(A) $\angle X$

(B) $\angle Y$

(C) $\angle Z$

(D) Cannot be determined

Question 16. If one angle of a triangle is $100^\circ$, the triangle is:

(A) Acute-angled

(B) Right-angled

(C) Obtuse-angled

(D) Equiangular

Question 17. The sum of an interior angle and its corresponding exterior angle at any vertex of a triangle is:

(A) $90^\circ$

(B) $180^\circ$

(C) $270^\circ$

(D) $360^\circ$

Question 18. If the three angles of a triangle are equal, the triangle is:

(A) Scalene

(B) Isosceles

(C) Equilateral

(D) Right-angled

Question 19. The smallest angle in a triangle is opposite the:

(A) Largest side

(B) Smallest side

(C) Medium side

(D) Hypotenuse

Question 20. In $\triangle$ABC, $\angle A = 70^\circ$, $\angle B = 50^\circ$. Which side is the shortest?

(A) AB

(B) BC

(C) AC

(D) Cannot be determined

Question 21. An exterior angle of a triangle can never be:

(A) Equal to an opposite interior angle

(B) Less than an opposite interior angle

(C) Greater than either of the opposite interior angles

(D) $90^\circ$

Question 1. The Pythagorean theorem applies specifically to which type of triangle?

(A) Acute-angled triangles

(B) Obtuse-angled triangles

(C) Right-angled triangles

(D) Equilateral triangles

Question 2. In a right-angled triangle, the side opposite the right angle is called the:

(A) Leg

(B) Altitude

(C) Hypotenuse

(D) Base

Question 3. According to the Pythagorean theorem, in a right-angled triangle with legs of length $a$ and $b$ and hypotenuse of length $c$, the relationship is:

(A) $a + b = c$

(B) $a^2 + b^2 = c^2$

(C) $a^2 \times b^2 = c^2$

(D) $a^2 + c^2 = b^2$

Question 4. A triangle has sides of lengths 6 cm, 8 cm, and 10 cm. Is it a right-angled triangle?

(A) Yes

(B) No

(C) Cannot be determined

(D) Only if the angles are $30^\circ, 60^\circ, 90^\circ$

Question 5. In a right-angled triangle, if the legs are 5 units and 12 units, the length of the hypotenuse is:

(A) 13 units

(B) 17 units

(C) $\sqrt{119}$ units

(D) $\sqrt{169}$ which is 13 units

Question 6. If the hypotenuse of a right-angled triangle is 25 units and one leg is 7 units, the length of the other leg is:

(A) 18 units

(B) 24 units

(C) $\sqrt{674}$ units

(D) 32 units

Question 7. The converse of the Pythagorean theorem states that if the square of one side of a triangle is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a:

(A) Acute angle

(B) Obtuse angle

(C) Right angle

(D) Straight angle

Question 8. A ladder 13 metres long is placed against a wall so that the foot of the ladder is 5 metres away from the wall. How high up the wall does the ladder reach?

(A) 8 metres

(B) 12 metres

(C) 14 metres

(D) $\sqrt{194}$ metres

Question 9. A triangle has sides of lengths $a$, $b$, and $c$. If $a^2 + b^2 < c^2$, then the angle opposite side $c$ is a(n):

(A) Acute angle

(B) Right angle

(C) Obtuse angle

(D) Straight angle

Question 10. A triangle has sides of lengths $a$, $b$, and $c$. If $a^2 + b^2 > c^2$, then the angle opposite side $c$ is a(n):

(A) Acute angle

(B) Right angle

(C) Obtuse angle

(D) Reflex angle

Question 11. Which of the following sets of side lengths could form a right-angled triangle?

(A) 2, 3, 4

(B) 3, 4, 5

(C) 4, 5, 6

(D) 5, 6, 7

Question 12. In an isosceles right-angled triangle, if the equal sides are 7 units each, what is the length of the hypotenuse?

(A) 7 units

(B) 14 units

(C) $\sqrt{98}$ units or $7\sqrt{2}$ units

(D) 49 units

Question 13. A square park has a diagonal path of length 20 metres. What is the approximate side length of the park?

(A) 10 metres

(B) $10\sqrt{2}$ metres (approx 14.14 m)

(C) 15 metres

(D) 20 metres

Question 14. In $\triangle$ABC, $\angle B = 90^\circ$. If AB = 8 cm and BC = 6 cm, what is the length of AC?

(A) 10 cm

(B) 14 cm

(C) $\sqrt{28}$ cm

(D) $\sqrt{100}$ which is 10 cm

Question 15. Which of the following is a Pythagorean triplet?

(A) (1, 2, 3)

(B) (2, 3, 4)

(C) (5, 12, 13)

(D) (6, 7, 8)

Question 16. The Pythagorean theorem is a special case of the law of cosines when the angle is:

(A) $0^\circ$

(B) $90^\circ$

(C) $180^\circ$

(D) $360^\circ$

Question 17. The area of the square on the hypotenuse of a right-angled triangle is equal to the sum of the areas of the squares on the other two sides. This is a visual interpretation of the:

(A) Angle sum property

(B) Exterior angle property

(C) Pythagorean theorem

(D) Triangle inequality

Question 18. A rope of length 15 metres is tied from the top of a pole to a point on the ground 9 metres away from the base of the pole. Assuming the pole is vertical, what is the height of the pole?

(A) 6 metres

(B) 12 metres

(C) $\sqrt{144}$ which is 12 metres

(D) 24 metres

Question 19. If the sides of a triangle are $k \cdot a, k \cdot b, k \cdot c$ where $(a, b, c)$ is a Pythagorean triplet and $k$ is a positive number, then the triangle is:

(A) Acute-angled

(B) Obtuse-angled

(C) Right-angled

(D) Not a triangle

Question 20. A rectangle has sides of length 7 cm and 24 cm. What is the length of its diagonal?

(A) 25 cm

(B) 31 cm

(C) $\sqrt{576+49}$ cm

(D) Both A and C

Question 1. Two geometric figures are congruent if they have the same:

(A) Shape

(B) Size

(C) Position

(D) Shape and size

Question 2. Which of the following is an example of congruent figures?

(A) A photograph and its enlargement

(B) Two copies of the same ₹ 10 coin

(C) A triangle and a square

(D) A sphere and a cube

Question 3. Two line segments are congruent if they have the same:

(A) Direction

(B) Position

(C) Length

(D) Endpoint

Question 4. Two angles are congruent if they have the same:

(A) Vertex

(B) Arms

(C) Measure

(D) Orientation

Question 5. Two triangles are congruent if their corresponding sides and corresponding angles are:

(A) Proportional

(B) Complementary

(C) Supplementary

(D) Equal

Question 6. Which congruence criterion states that if two sides and the included angle of one triangle are equal to the corresponding two sides and the included angle of another triangle, then the triangles are congruent?

(A) SSS

(B) ASA

(C) SAS

(D) AAS

Question 7. Which congruence criterion states that if all three sides of one triangle are equal to the corresponding three sides of another triangle, then the triangles are congruent?

(A) SSS

(B) SAS

(C) ASA

(D) AAS

Question 8. Which congruence criterion states that if two angles and the included side of one triangle are equal to the corresponding two angles and the included side of another triangle, then the triangles are congruent?

(A) SSS

(B) ASA

(C) SAS

(D) AAS

Question 9. Which congruence criterion states that if two angles and one side (not necessarily included) of one triangle are equal to the corresponding two angles and one side of another triangle, then the triangles are congruent?

(A) SSS

(B) ASA

(C) SAS

(D) AAS

Question 10. Which congruence criterion is used specifically for right-angled triangles, involving the hypotenuse and one side?

(A) SSS

(B) ASA

(C) RHS

(D) AAS

Question 11. The abbreviation CPCTC stands for:

(A) Corresponding Parts of Congruent Triangles are Congruent

(B) Congruent Polygons Create Triangle Congruence

(C) Circles, Points, Triangles, and Corresponding parts

(D) Common Property for Triangle Congruence

Question 12. If $\triangle \text{ABC} \cong \triangle \text{XYZ}$, which of the following statements is NOT necessarily true?

(A) AB = XY

(B) $\angle B = \angle Y$

(C) AC = YZ

(D) Area of $\triangle \text{ABC} =$ Area of $\triangle \text{XYZ}$

Question 13. If two triangles are congruent by the ASA criterion, it means:

(A) Two sides and the included angle are equal.

(B) Two angles and the included side are equal.

(C) All three sides are equal.

(D) Two angles and a non-included side are equal.

Question 14. If $\triangle \text{PQR} \cong \triangle \text{STU}$ by SSS criterion, which angle must be equal to $\angle S$?

(A) $\angle P$

(B) $\angle Q$

(C) $\angle R$

(D) Cannot be determined

Question 15. In $\triangle \text{ABC}$ and $\triangle \text{DEF}$, if AB = DE, BC = EF, and $\angle B = \angle E$, by which criterion are the triangles congruent?

(A) SSS

(B) SAS

(C) ASA

(D) AAS

Question 16. Congruent figures have the same shape and the same:

(A) Colour

(B) Orientation

(C) Volume

(D) Size

Question 17. If two circles have the same radius, they are:

(A) Similar

(B) Congruent

(C) Both similar and congruent

(D) Neither similar nor congruent

Question 18. If $\triangle \text{LMN} \cong \triangle \text{PQR}$, then $\angle L$ corresponds to:

(A) $\angle P$

(B) $\angle Q$

(C) $\angle R$

(D) $\angle M$

Question 19. In the RHS congruence criterion for right-angled triangles, 'H' stands for:

(A) Height

(B) Hypotenuse

(C) Horizontal

(D) Half

Question 20. If two squares have the same side length, they are:

(A) Similar but not congruent

(B) Congruent but not necessarily similar

(C) Both congruent and similar

(D) Neither congruent nor similar

Question 21. If two line segments are congruent, it means their lengths are:

(A) Proportional

(B) Equal

(C) Different

(D) Complementary

Question 1. Two figures are similar if they have the same:

(A) Shape and same size

(B) Shape but different size

(C) Size but different shape

(D) Neither shape nor size are related

Question 2. For two triangles to be similar, their corresponding angles must be:

(A) Complementary

(B) Supplementary

(C) Equal

(D) Proportional

Question 3. For two triangles to be similar, their corresponding sides must be:

(A) Equal

(B) Parallel

(C) Perpendicular

(D) In the same ratio (proportional)

Question 4. The AA similarity criterion states that if two angles of one triangle are respectively equal to two angles of another triangle, then the triangles are:

(A) Congruent

(B) Similar

(C) Neither congruent nor similar

(D) Equilateral

Question 5. The SSS similarity criterion states that if the corresponding sides of two triangles are proportional, then the triangles are:

(A) Congruent

(B) Similar

(C) Right-angled

(D) Equilateral

Question 6. The SAS similarity criterion states that if one angle of a triangle is equal to one angle of the other triangle and the sides including these angles are proportional, then the two triangles are:

(A) Congruent

(B) Similar

(C) Isosceles

(D) Equilateral

Question 7. The Basic Proportionality Theorem (BPT), also known as Thales Theorem, deals with a line drawn parallel to one side of a triangle intersecting the other two sides. It states that this line divides the other two sides:

(A) Equally

(B) Proportionally

(C) Perpendicularly

(D) Congruently

Question 8. In $\triangle$ABC, a line DE is drawn parallel to BC, intersecting AB at D and AC at E. According to BPT:

(A) $\frac{AD}{DB} = \frac{AE}{EC}$

(B) $\frac{AD}{AB} = \frac{AE}{AC}$

(C) DE = BC

(D) $\angle ADE = \angle AED$

Question 9. The converse of the Basic Proportionality Theorem states that if a line divides any two sides of a triangle in the same ratio, then the line is _____ to the third side.

(A) Perpendicular

(B) Parallel

(C) Intersecting

(D) Congruent

Question 10. Are two congruent triangles always similar?

(A) Yes

(B) No

(C) Only if they are equilateral

(D) Only if they are right-angled

Question 11. Are two similar triangles always congruent?

(A) Yes

(B) No

(C) Only if the ratio of corresponding sides is 1:1

(D) Only if their angles are $60^\circ, 60^\circ, 60^\circ$

Question 12. If $\triangle \text{ABC} \sim \triangle \text{PQR}$, then $\angle A$ is equal to:

(A) $\angle P$

(B) $\angle Q$

(C) $\angle R$

(D) $\angle B$

Question 13. If $\triangle \text{ABC} \sim \triangle \text{PQR}$, then the ratio $\frac{AB}{PQ}$ is equal to:

(A) $\frac{AC}{QR}$

(B) $\frac{BC}{PR}$

(C) $\frac{AC}{PR}$

(D) $\frac{AB}{QR}$

Question 14. All equilateral triangles are:

(A) Congruent

(B) Similar

(C) Both congruent and similar

(D) Neither congruent nor similar

Question 15. If the sides of two triangles are in the ratio 2:3, what is the ratio of their corresponding angles?

(A) 2:3

(B) 4:9

(C) 1:1 (equal)

(D) Depends on the type of triangle

Question 16. In $\triangle \text{ABC}$, D and E are points on AB and AC respectively such that $\frac{AD}{DB} = \frac{AE}{EC}$. If $\angle ADE = 70^\circ$, find $\angle ABC$.

(A) $70^\circ$

(B) $110^\circ$

(C) $40^\circ$

(D) Cannot be determined

Question 17. Which criterion for similarity of triangles is not typically listed as one of the primary criteria?

(A) AAA (or AA)

(B) SSS

(C) SAS

(D) ASA

Question 18. If the ratio of corresponding sides of two similar triangles is $1:2$, what is the ratio of their perimeters?

(A) 1:2

(B) 1:4

(C) 2:1

(D) 1:$\sqrt{2}$

Question 19. All circles are:

(A) Congruent

(B) Similar

(C) Both congruent and similar

(D) Neither congruent nor similar

Question 20. If a line is drawn parallel to one side of a triangle, the triangle formed by the segment cutting the other two sides and the original triangle are:

(A) Congruent

(B) Similar

(C) Both congruent and similar

(D) Neither congruent nor similar

Question 1. If two triangles are similar, the ratio of their areas is equal to the square of the ratio of their corresponding:

(A) Angles

(B) Perimeters

(C) Altitudes

(D) Sides

Question 2. If the ratio of corresponding sides of two similar triangles is $m:n$, then the ratio of their areas is:

(A) $m:n$

(B) $m^2:n^2$

(C) $n:m$

(D) $\sqrt{m}:\sqrt{n}$

Question 3. The areas of two similar triangles are $36 \text{ cm}^2$ and $81 \text{ cm}^2$. What is the ratio of their corresponding sides?

(A) 6:9

(B) 2:3

(C) $\sqrt{36}:\sqrt{81}$

(D) All of the above

Question 4. If the ratio of the perimeters of two similar triangles is $4:5$, what is the ratio of their areas?

(A) 4:5

(B) 16:25

(C) 2:$\sqrt{5}$

(D) 25:16

Question 5. In a right-angled triangle, if an altitude is drawn from the vertex with the right angle to the hypotenuse, it divides the original triangle into two smaller triangles that are:

(A) Congruent to each other

(B) Similar to each other

(C) Congruent to the original triangle

(D) Similar to the original triangle

Question 6. In a right triangle ABC, right-angled at B, an altitude BD is drawn to the hypotenuse AC. Which similarity relationship is true?

(A) $\triangle \text{ADB} \sim \triangle \text{BDC}$

(B) $\triangle \text{ADB} \sim \triangle \text{ABC}$

(C) $\triangle \text{BDC} \sim \triangle \text{ABC}$

(D) All of the above

Question 7. If the ratio of areas of two similar triangles is $9:16$, what is the ratio of their corresponding medians?

(A) 9:16

(B) 3:4

(C) $\sqrt{9}:\sqrt{16}$

(D) Both B and C

Question 8. A model of a building is made using a scale of 1:100. If the height of the model is 5 cm, what is the actual height of the building?

(A) 50 cm

(B) 5 metres

(C) 50 metres

(D) 500 metres

Question 9. Two triangles are similar. The area of the larger triangle is $100 \text{ cm}^2$ and the area of the smaller triangle is $64 \text{ cm}^2$. If a side of the smaller triangle is 8 cm, what is the length of the corresponding side of the larger triangle?

(A) 10 cm

(B) 12.5 cm

(C) 16 cm

(D) 20 cm

Question 10. In right triangle ABC, right-angled at B, if BD is the altitude to AC, then $BD^2$ is equal to:

(A) $AD \times DC$

(B) $AB \times BC$

(C) $AC \times AD$

(D) $AD + DC$

Question 11. Two poles of heights 10 m and 15 m stand upright on a plane ground. If the distance between their bases is 12 m, what is the distance between their tops? (Hint: Use similarity or Pythagorean theorem on a right triangle formed by extending one pole and drawing a horizontal line)

(A) 13 m

(B) 15 m

(C) 17 m

(D) $\sqrt{144+25}$ which is 13 m

Question 12. The ratio of areas of two similar triangles is equal to the square of the ratio of their corresponding:

(A) Angle bisectors

(B) Altitudes

(C) Medians

(D) All of the above

Question 13. If $\triangle \text{XYZ} \sim \triangle \text{PQR}$ and Area($\triangle \text{XYZ}$) : Area($\triangle \text{PQR}$) = 4:9, and XY = 6 cm, then PQ is:

(A) 9 cm

(B) 12 cm

(C) 4 cm

(D) 8 cm

Question 14. If two triangles are similar with a scale factor of $k$ (ratio of corresponding sides is $k:1$), then the ratio of their areas is:

(A) $k:1$

(B) $k^2:1$

(C) $\sqrt{k}:1$

(D) $1:k$

Question 15. Similarity is used in mapping where distances on the map are proportional to the actual distances on the ground. If a map uses a scale of 1 cm = 100 metres, and a triangular region on the map has an area of $5 \text{ cm}^2$, what is the actual area of the region?

(A) $500 \text{ m}^2$

(B) $5000 \text{ m}^2$

(C) $50000 \text{ m}^2$

(D) $500000 \text{ m}^2$

Question 16. In right triangle ABC, right-angled at B, BD is the altitude to AC. If AD = 4 cm and DC = 9 cm, then the length of BD is:

(A) 5 cm

(B) 6 cm

(C) 6.5 cm

(D) 13 cm

Question 17. If two similar triangles have areas in the ratio $a:b$, then the ratio of their corresponding altitudes is:

(A) $a:b$

(B) $a^2:b^2$

(C) $\sqrt{a}:\sqrt{b}$

(D) $b:a$

Question 18. Similarity can be used to find the height of tall objects (like trees or buildings) by comparing the length of their shadows with the shadow of an object of known height. This application relies on the concept of:

(A) Congruence

(B) Parallel lines

(C) Similar triangles

(D) Area calculation

Question 19. If $\triangle \text{PQR} \sim \triangle \text{XYZ}$ and PQ:XY = 1:3. If the area of $\triangle \text{PQR}$ is $10 \text{ cm}^2$, what is the area of $\triangle \text{XYZ}$?

(A) $30 \text{ cm}^2$

(B) $60 \text{ cm}^2$

(C) $90 \text{ cm}^2$

(D) $100 \text{ cm}^2$

Question 20. The ratio of areas of two similar triangles is always positive. True or False?

(A) True

(B) False

(C) Depends on the triangles

(D) Only if they are congruent

Question 21. In right triangle ABC, right-angled at B, BD is the altitude to AC. Then $\triangle \text{ABD}$ and $\triangle \text{ABC}$ are similar. The ratio of their corresponding sides AD and AB is equal to:

(A) AB/BC

(B) BD/BC

(C) AB/AC

(D) AD/BD

Question 1. A quadrilateral is a polygon with:

(A) 3 sides

(B) 4 sides

(C) 5 sides

(D) 6 sides

Question 2. The sum of the interior angles of any convex quadrilateral is:

(A) $180^\circ$

(B) $360^\circ$

(C) $540^\circ$

(D) $720^\circ$

Question 3. A quadrilateral with exactly one pair of parallel sides is called a:

(A) Parallelogram

(B) Rhombus

(C) Trapezium

(D) Kite

Question 4. A quadrilateral where both pairs of opposite sides are parallel is called a:

(A) Trapezium

(B) Kite

(C) Rectangle

(D) Parallelogram

Question 5. Which of the following is a property of ALL parallelograms?

(A) All sides are equal.

(B) All angles are $90^\circ$.

(C) Opposite angles are equal.

(D) Diagonals are equal.

Question 6. In a parallelogram, the diagonals:

(A) Are perpendicular bisectors of each other.

(B) Are equal in length.

(C) Bisect each other.

(D) Bisect the angles.

Question 7. A parallelogram with all four angles equal to $90^\circ$ is called a:

(A) Rhombus

(B) Square

(C) Rectangle

(D) Trapezoid

Question 8. A parallelogram with all four sides equal is called a:

(A) Rectangle

(B) Square

(C) Rhombus

(D) Kite

Question 9. A quadrilateral that is both a rectangle and a rhombus is a:

(A) Parallelogram

(B) Square

(C) Trapezium

(D) Kite

Question 10. In a rhombus, the diagonals are:

(A) Equal and bisect each other

(B) Perpendicular and bisect each other

(C) Equal and perpendicular

(D) Neither equal nor perpendicular

Question 11. Which of the following is always a parallelogram?

(A) Trapezium

(B) Kite

(C) Rectangle

(D) Isosceles Trapezium

Question 12. If the diagonals of a quadrilateral bisect each other, the quadrilateral is a:

(A) Trapezium

(B) Kite

(C) Parallelogram

(D) Rhombus (Rhombus is a type of parallelogram)

Question 13. If the diagonals of a parallelogram are equal, it is a:

(A) Rhombus

(B) Square

(C) Rectangle

(D) Trapezium

Question 14. In a kite, the diagonals are:

(A) Equal

(B) Parallel

(C) Perpendicular

(D) Bisect each other

Question 15. A square is a special type of:

(A) Rhombus

(B) Rectangle

(C) Parallelogram

(D) All of the above

Question 16. In a parallelogram ABCD, if $\angle A = 70^\circ$, then $\angle B$ is:

(A) $70^\circ$

(B) $110^\circ$

(C) $90^\circ$

(D) $35^\circ$

Question 17. In a parallelogram ABCD, if AB = 8 cm and BC = 5 cm, then the perimeter of the parallelogram is:

(A) 13 cm

(B) 26 cm

(C) 32 cm

(D) 40 cm

Question 18. Which quadrilateral has diagonals that are equal and perpendicular bisectors of each other?

(A) Rectangle

(B) Rhombus

(C) Square

(D) Parallelogram

Question 19. A quadrilateral whose four sides are equal is a:

(A) Rectangle

(B) Parallelogram

(C) Rhombus

(D) Square (Square is a type of rhombus)

Question 20. The adjacent angles of a parallelogram are:

(A) Equal

(B) Complementary

(C) Supplementary

(D) Right angles

Question 21. In a trapezium, the non-parallel sides are equal. This type of trapezium is called:

(A) Right trapezium

(B) Scalene trapezium

(C) Isosceles trapezium

(D) Parallel trapezium

Question 1. The Mid-Point Theorem states that the line segment joining the midpoints of two sides of a triangle is parallel to the third side and:

(A) Equal to the third side

(B) Half of the third side

(C) Twice the third side

(D) Perpendicular to the third side

Question 2. In $\triangle$ABC, D and E are midpoints of sides AB and AC respectively. According to the Mid-Point Theorem, DE is parallel to:

(A) AB

(B) AC

(C) BC

(D) AE

Question 3. In $\triangle$PQR, M and N are midpoints of PQ and PR respectively. If MN = 6 cm, what is the length of QR?

(A) 3 cm

(B) 6 cm

(C) 12 cm

(D) 18 cm

Question 4. The converse of the Mid-Point Theorem states that a line drawn through the midpoint of one side of a triangle, parallel to another side, intersects the third side at its:

(A) Vertex

(B) Midpoint

(C) Endpoint

(D) Any point

Question 5. In $\triangle$XYZ, P is the midpoint of XY. A line through P parallel to YZ intersects XZ at Q. According to the converse of the Mid-Point Theorem, Q is the midpoint of:

(A) XY

(B) YZ

(C) XZ

(D) PQ

Question 6. In a quadrilateral ABCD, P, Q, R, and S are the midpoints of sides AB, BC, CD, and DA respectively. The figure PQRS formed by joining these midpoints is always a:

(A) Square

(B) Rectangle

(C) Rhombus

(D) Parallelogram

Question 7. In the parallelogram PQRS, if L and M are the midpoints of sides PQ and RS respectively, then the line segment LM divides the parallelogram into two:

(A) Congruent triangles

(B) Similar triangles

(C) Congruent parallelograms

(D) Trapezoids

Question 8. The Mid-Point Theorem can be proven using the concept of:

(A) Similarity of triangles

(B) Congruence of triangles

(C) Pythagorean theorem

(D) Circle properties

Question 9. If a line segment joins the midpoints of two sides of a triangle, its length is proportional to the third side with a ratio of:

(A) 1:1

(B) 1:2

(C) 2:1

(D) 1:$\sqrt{2}$

Question 10. In $\triangle$ABC, D is the midpoint of AB. A line through D parallel to BC intersects AC at E. If AC = 10 cm, what is the length of AE?

(A) 2.5 cm

(B) 5 cm

(C) 10 cm

(D) 20 cm

Question 11. In the quadrilateral PQRS, if P, Q, R, S are midpoints of the sides of quadrilateral ABCD, and AC is a diagonal of ABCD, then PQ is parallel to AC and PQ = $\frac{1}{2}$ AC. This is an application of the:

(A) Basic Proportionality Theorem

(B) Pythagorean Theorem

(C) Angle Sum Property

(D) Mid-Point Theorem

Question 12. If a line segment connects the midpoints of two sides of a triangle, it is parallel to the third side. What is the reason for this parallelism?

(A) Definition of parallel lines

(B) Converse of BPT

(C) Corresponding angles are equal (derived from the proof using similarity or congruence)

(D) Alternate interior angles are equal

Question 13. The Mid-Point Theorem can be applied to find relationships between the sides of a triangle and the segment connecting two of its:

(A) Vertices

(B) Angles

(C) Midpoints of sides

(D) Altitudes

Question 14. Consider a triangle with vertices A, B, C. Let D be the midpoint of AB and E be the midpoint of AC. Which statement is true?

(A) DE || AB

(B) DE || AC

(C) DE || BC

(D) DE is perpendicular to BC

Question 15. In $\triangle$ABC, D, E, F are midpoints of sides AB, BC, CA respectively. The triangle DEF is formed by joining the midpoints. The perimeter of $\triangle$DEF is _____ the perimeter of $\triangle$ABC.

(A) Equal to

(B) Half of

(C) Twice

(D) One-third of

Question 16. In $\triangle$ABC, D, E, F are midpoints of sides AB, BC, CA respectively. The area of $\triangle$DEF is _____ the area of $\triangle$ABC.

(A) Equal to

(B) Half of

(C) One-fourth of

(D) One-third of

Question 17. The converse of the Mid-Point Theorem is often used to prove that a point is a:

(A) Vertex

(B) Midpoint

(C) Centroid

(D) Orthocentre

Question 18. If in $\triangle$PQR, S is the midpoint of PQ, and a line through S parallel to QR intersects PR at T, then PT:TR is:

(A) 1:1

(B) 1:2

(C) 2:1

(D) 1:3

Question 19. The application of the Mid-Point Theorem in finding the type of quadrilateral formed by joining the midpoints of a given quadrilateral demonstrates a relationship between the given quadrilateral and its:

(A) Diagonals

(B) Sides

(C) Angles

(D) Area

Question 20. If the figure formed by joining the midpoints of a quadrilateral is a rhombus, then the diagonals of the original quadrilateral must be:

(A) Equal

(B) Perpendicular

(C) Parallel

(D) Bisected

Question 1. The area of a plane figure is the measure of the region enclosed by its:

(A) Vertices

(B) Boundary

(C) Diagonals

(D) Perimeter

Question 2. Two figures having the same area are called:

(A) Congruent figures

(B) Similar figures

(C) Equal in area figures

(D) Identical figures

Question 3. If two figures are congruent, are they equal in area?

(A) Yes, always

(B) No, never

(C) Sometimes

(D) Depends on their shape

Question 4. Which statement is true about figures on the same base and between the same parallels?

(A) They are always congruent.

(B) They always have the same perimeter.

(C) They always have the same area.

(D) They are always similar.

Question 5. Parallelograms on the same base and between the same parallels are:

(A) Congruent

(B) Similar

(C) Equal in area

(D) Equal in perimeter

Question 6. Triangles on the same base (or equal bases) and between the same parallels are:

(A) Congruent

(B) Similar

(C) Equal in area

(D) Equal in perimeter

Question 7. If a triangle and a parallelogram are on the same base and between the same parallels, then the area of the triangle is _____ the area of the parallelogram.

(A) Equal to

(B) Half of

(C) Twice

(D) One-third of

Question 8. The area of a triangle is given by $\frac{1}{2} \times \text{base} \times \text{height}$. If two triangles have the same base and the same height, their areas are:

(A) Proportional

(B) Different

(C) Equal

(D) Cannot be compared

Question 9. In parallelogram ABCD, diagonal AC divides it into two triangles, $\triangle \text{ABC}$ and $\triangle \text{ADC}$. What is the relationship between the areas of these two triangles?

(A) Area($\triangle \text{ABC}$) > Area($\triangle \text{ADC}$)

(B) Area($\triangle \text{ABC}$) < Area($\triangle \text{ADC}$)

(C) Area($\triangle \text{ABC}$) = Area($\triangle \text{ADC}$)

(D) Cannot be determined

Question 10. The area of a parallelogram is given by $\text{base} \times \text{height}$. If two parallelograms have the same base and same height, their areas are:

(A) Different

(B) Equal

(C) Proportional

(D) Half of each other

Question 11. If a median is drawn in a triangle, it divides the triangle into two triangles that are:

(A) Congruent

(B) Similar

(C) Equal in area

(D) Right-angled

Question 12. In $\triangle$ABC, D is the midpoint of BC. Then Area($\triangle \text{ABD}$) is equal to:

(A) Area($\triangle \text{ABC}$)

(B) $\frac{1}{2}$ Area($\triangle \text{ABC}$)

(C) $\frac{1}{3}$ Area($\triangle \text{ABC}$)

(D) $\frac{1}{4}$ Area($\triangle \text{ABC}$)

Question 13. If two triangles have the same area and the same base, they must lie between the same:

(A) Perpendiculars

(B) Lines

(C) Parallels

(D) Medians

Question 14. If two parallelograms have the same area and are on the same base, they must lie between the same:

(A) Vertices

(B) Diagonals

(C) Parallels

(D) Sides

Question 15. Area is always a non-negative value. True or False?

(A) True

(B) False

(C) Depends on the coordinate system

(D) Only for convex figures

Question 16. A rectangle and a parallelogram stand on the same base and between the same parallels. Which figure has a larger area?

(A) The rectangle

(B) The parallelogram

(C) They have equal area

(D) Depends on the angle of the parallelogram

Question 17. If the area of $\triangle$ABC is $20 \text{ cm}^2$, and D is the midpoint of BC, what is the area of $\triangle$ABD?

(A) $5 \text{ cm}^2$

(B) $10 \text{ cm}^2$

(C) $20 \text{ cm}^2$

(D) $40 \text{ cm}^2$

Question 18. If a figure is moved or rotated without changing its shape or size (rigid transformation), its area:

(A) Changes

(B) Remains the same

(C) Becomes zero

(D) Doubles

Question 19. Two triangles are on the same base and have equal area. What can you say about their vertices opposite the common base?

(A) They must coincide.

(B) They must lie on a line parallel to the base.

(C) They must lie on a perpendicular bisector of the base.

(D) They must form an isosceles triangle with the endpoints of the base.

Question 20. The area of a polygonal region is typically measured in:

(A) Units of length (e.g., cm, m)

(B) Square units (e.g., $\text{cm}^2, \text{m}^2$)

(C) Cubic units (e.g., $\text{cm}^3, \text{m}^3$)

(D) Degrees ($\circ$)

Question 1. A circle is a set of all points in a plane that are equidistant from a fixed point. This fixed point is called the:

(A) Radius

(B) Diameter

(C) Circumference

(D) Centre

Question 2. The fixed distance from the centre to any point on the circle is called the:

(A) Diameter

(B) Chord

(C) Radius

(D) Arc

Question 3. A line segment passing through the centre of the circle and having its endpoints on the circle is called the:

(A) Radius

(B) Chord

(C) Diameter

(D) Tangent

Question 4. The perimeter of a circle is called its:

(A) Area

(B) Chord

(C) Circumference

(D) Diameter

Question 5. A line segment joining any two points on the circle is called a:

(A) Radius

(B) Diameter

(C) Chord

(D) Secant

Question 6. The longest chord of a circle is the:

(A) Radius

(B) Diameter

(C) Secant

(D) Tangent

Question 7. A part of the circumference of a circle is called a(n):

(A) Chord

(B) Segment

(C) Sector

(D) Arc

Question 8. The region between a chord and its corresponding arc is called a:

(A) Sector

(B) Segment

(C) Quadrant

(D) Annulus

Question 9. The region between two radii and the corresponding arc is called a:

(A) Segment

(B) Sector

(C) Chord

(D) Circumference

Question 10. Points that lie outside the circle are in the:

(A) Interior

(B) Exterior

(C) Boundary

(D) Centre

Question 11. The boundary of a circle is the circle itself. Points on the circle are on its:

(A) Interior

(B) Exterior

(C) Boundary

(D) Centre

Question 12. Two circles are congruent if they have the same:

(A) Centre

(B) Circumference

(C) Area

(D) All of the above (equal radii implies equal circumference and area)

Question 13. An arc whose endpoints are the endpoints of a diameter is called a:

(A) Minor arc

(B) Major arc

(C) Semicircle

(D) Sector

Question 14. In a circle, the relationship between diameter ($d$) and radius ($r$) is:

(A) $d = r$

(B) $d = 2r$

(C) $d = r/2$

(D) $d = r^2$

Question 15. The formula for the circumference of a circle with radius $r$ is:

(A) $\pi r^2$

(B) $2\pi r$

(C) $\pi d$

(D) Both B and C

Question 16. Congruent arcs in the same circle have:

(A) The same length

(B) The same measure (angle subtended at centre)

(C) Subtend equal angles at the centre

(D) All of the above

Question 17. A segment of a circle smaller than a semicircle is called a:

(A) Major segment

(B) Minor segment

(C) Quarter segment

(D) Semicircular segment

Question 18. The interior of a circle consists of all points whose distance from the centre is _____ the radius.

(A) Greater than

(B) Less than

(C) Equal to

(D) Greater than or equal to

Question 19. If two circles have the same radius, they are:

(A) Similar

(B) Congruent

(C) Different

(D) concentric

Question 20. The ratio of the circumference of a circle to its diameter is a constant value denoted by:

(A) $e$

(B) $\pi$

(C) $\phi$

(D) $\gamma$

Question 1. The angle subtended by a chord at the centre of a circle is:

(A) Equal to the angle subtended by the same chord at any point on the remaining part of the circle.

(B) Half the angle subtended by the same chord at any point on the remaining part of the circle.

(C) Twice the angle subtended by the same chord at any point on the remaining part of the circle.

(D) Unrelated to the angle subtended at the circumference.

Question 2. Equal chords of a circle subtend equal angles at the:

(A) Circumference

(B) Centre

(C) Any point on the circle

(D) Interior of the circle

Question 3. The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle. True or False?

(A) True

(B) False

(C) Only for major arcs

(D) Only for minor arcs

Question 4. Angles in the same segment of a circle are:

(A) Complementary

(B) Supplementary

(C) Equal

(D) Proportional

Question 5. The angle in a semicircle is always a:

(A) Acute angle

(B) Obtuse angle

(C) Right angle ($90^\circ$)

(D) Straight angle

Question 6. Chords equidistant from the centre of a circle are:

(A) Parallel

(B) Perpendicular

(C) Equal in length

(D) Unequal in length

Question 7. The perpendicular from the centre of a circle to a chord:

(A) Bisects the chord

(B) Bisects the angle subtended by the chord at the centre

(C) Both A and B

(D) None of the above

Question 8. If the angle subtended by a chord at the centre is $120^\circ$, what is the angle subtended by the same chord at any point on the major arc?

(A) $60^\circ$

(B) $120^\circ$

(C) $240^\circ$

(D) $30^\circ$

Question 9. In a circle, if two chords are equal in length, then they are _____ from the centre.

(A) At different distances

(B) Equidistant

(C) Parallel

(D) Perpendicular

Question 10. The angle subtended by a diameter at any point on the circumference is:

(A) $0^\circ$

(B) $90^\circ$

(C) $180^\circ$

(D) $360^\circ$

Question 11. If the angles subtended by two chords at the centre of a circle are equal, then the chords are:

(A) Parallel

(B) Perpendicular

(C) Equal in length

(D) Different in length

Question 12. The line joining the centre of a circle to the midpoint of a chord is always _____ to the chord.

(A) Parallel

(B) Perpendicular

(C) Bisected by

(D) Twice the length of

Question 13. In a circle, if $\angle ABC = 40^\circ$ where A, B, C are points on the circle, and $\angle AOC$ is the angle subtended by arc AC at the centre O, then $\angle AOC =$

(A) $40^\circ$

(B) $80^\circ$

(C) $20^\circ$

(D) $160^\circ$

Question 14. The segment of a circle is the region between a chord and the corresponding arc. The angle subtended by the chord at any point on the *major* arc is $\theta$. The angle subtended by the same chord at any point on the *minor* arc is:

(A) $\theta$

(B) $180^\circ - \theta$

(C) $90^\circ - \theta$

(D) $180^\circ + \theta$

Question 15. Two distinct chords of a circle can bisect each other only if they are both:

(A) Equal

(B) Perpendicular

(C) Radii

(D) Diameters

Question 16. If a line intersects a circle at two distinct points, it is called a:

(A) Tangent

(B) Secant

(C) Chord

(D) Radius

Question 17. The angle in a major segment is:

(A) Acute

(B) Right

(C) Obtuse

(D) Reflex

Question 18. The angle in a minor segment is:

(A) Acute

(B) Right

(C) Obtuse

(D) Straight

Question 19. The locus of a point equidistant from two fixed points is a:

(A) Circle

(B) Line

(C) Perpendicular bisector

(D) Angle bisector

Question 20. How many circles can pass through two distinct points?

(A) One

(B) Two

(C) A finite number

(D) An infinite number

Question 1. A quadrilateral whose all four vertices lie on a circle is called a:

(A) Parallelogram

(B) Cyclic quadrilateral

(C) Rhombus

(D) Trapezium

Question 2. In a cyclic quadrilateral, the sum of each pair of opposite angles is:

(A) $90^\circ$

(B) $180^\circ$

(C) $270^\circ$

(D) $360^\circ$

Question 3. If ABCD is a cyclic quadrilateral, then $\angle A + \angle C =$

(A) $90^\circ$

(B) $180^\circ$

(C) $270^\circ$

(D) $360^\circ$

Question 4. In a cyclic quadrilateral, the exterior angle at a vertex is equal to the:

(A) Adjacent interior angle

(B) Opposite interior angle

(C) Sum of opposite interior angles

(D) Difference of opposite interior angles

Question 5. If the sum of any pair of opposite angles of a quadrilateral is $180^\circ$, then the quadrilateral is:

(A) A parallelogram

(B) A rhombus

(C) Cyclic

(D) A trapezium

Question 6. If ABCD is a cyclic quadrilateral and $\angle A = 80^\circ$, then $\angle C =$

(A) $80^\circ$

(B) $100^\circ$

(C) $180^\circ$

(D) $280^\circ$

Question 7. Can a parallelogram be a cyclic quadrilateral?

(A) Yes, always

(B) Yes, if it is a rectangle or a square

(C) No, never

(D) Only if it is a rhombus

Question 8. If a rhombus is a cyclic quadrilateral, what type of rhombus must it be?

(A) A square

(B) A parallelogram

(C) A kite

(D) A rectangle

Question 9. In cyclic quadrilateral PQRS, if $\angle P = 110^\circ$, $\angle Q = 70^\circ$, find $\angle R$ and $\angle S$.

(A) $\angle R = 70^\circ, \angle S = 110^\circ$

(B) $\angle R = 110^\circ, \angle S = 70^\circ$

(C) $\angle R = 70^\circ, \angle S = 70^\circ$

(D) $\angle R = 110^\circ, \angle S = 110^\circ$

Question 10. If three points are collinear, can they be vertices of a cyclic quadrilateral?

(A) Yes, always

(B) Yes, if the fourth point is on the line

(C) No, because all four vertices must lie on the circle

(D) Yes, if the quadrilateral is a trapezium

Question 11. The property that opposite angles of a cyclic quadrilateral are supplementary is a necessary and sufficient condition for a quadrilateral to be cyclic. True or False?

(A) True

(B) False

(C) Necessary but not sufficient

(D) Sufficient but not necessary

Question 12. In cyclic quadrilateral ABCD, if side AB is extended to point E, then the exterior angle $\angle CBE$ is equal to:

(A) $\angle A$

(B) $\angle B$

(C) $\angle C$

(D) $\angle D$

Question 13. A square is always a cyclic quadrilateral. True or False?

(A) True

(B) False

(C) Only if its side length is equal to the diameter

(D) Only if it is inscribed in the circle

Question 14. A rectangle is always a cyclic quadrilateral. True or False?

(A) True

(B) False

(C) Only if its side lengths are equal

(D) Only if its diagonal is equal to the diameter

Question 15. Can a trapezium be a cyclic quadrilateral?

(A) Yes, always

(B) Yes, if it is an isosceles trapezium

(C) No, never

(D) Only if its parallel sides are equal

Question 16. If a cyclic quadrilateral has two adjacent angles measuring $60^\circ$ and $120^\circ$, what are the measures of the other two angles?

(A) $60^\circ, 120^\circ$

(B) $120^\circ, 60^\circ$

(C) $90^\circ, 90^\circ$

(D) Cannot be determined

Question 17. In cyclic quadrilateral ABCD, the diagonals AC and BD intersect at point E. Which of the following statements is true?

(A) $\triangle \text{ABE} \sim \triangle \text{CDE}$

(B) $\triangle \text{ABE} \cong \triangle \text{CDE}$

(C) $\angle EAB = \angle ECD$

(D) Both A and C are true

Question 18. If a cyclic parallelogram is not a rectangle, then it must be a:

(A) Rhombus

(B) Square

(C) Isosceles Trapezium

(D) Such a parallelogram does not exist

Question 19. If all vertices of a quadrilateral lie on a circle, the circle is called the _____ circle of the quadrilateral.

(A) Inscribed

(B) Concentric

(C) Circumscribed

(D) Tangent

Question 20. Which of the following properties does a cyclic quadrilateral NOT necessarily have?

(A) Opposite angles are supplementary.

(B) All sides are equal.

(C) Vertices lie on a circle.

(D) Exterior angle is equal to the opposite interior angle.

Question 1. A line that intersects a circle at exactly one point is called a:

(A) Secant

(B) Chord

(C) Tangent

(D) Diameter

Question 2. A line that intersects a circle at two distinct points is called a:

(A) Tangent

(B) Secant

(C) Radius

(D) Point of contact

Question 3. The point where a tangent line touches a circle is called the:

(A) Vertex

(B) Centre

(C) Point of intersection

(D) Point of contact

Question 4. A tangent to a circle is perpendicular to the radius through the:

(A) Centre

(B) Any point on the tangent

(C) Point of contact

(D) Midpoint of the tangent

Question 5. How many tangents can be drawn to a circle from a point lying inside the circle?

(A) Zero

(B) One

(C) Two

(D) Infinite

Question 6. How many tangents can be drawn to a circle from a point lying on the circle?

(A) Zero

(B) One

(C) Two

(D) Infinite

Question 7. How many tangents can be drawn to a circle from a point lying outside the circle?

(A) Zero

(B) One

(C) Two

(D) Infinite

Question 8. The lengths of the tangents drawn from an external point to a circle are:

(A) Unequal

(B) Complementary

(C) Supplementary

(D) Equal

Question 9. If two tangents are drawn to a circle from an external point P, touching the circle at A and B, then $\triangle \text{PAB}$ is always:

(A) Right-angled

(B) Equilateral

(C) Isosceles

(D) Scalene

Question 10. In a circle, two parallel tangents are drawn. A third tangent is drawn such that it touches the circle and intersects the two parallel tangents. The segment of the third tangent between the two parallel tangents subtends an angle at the centre of:

(A) $60^\circ$

(B) $90^\circ$

(C) $120^\circ$

(D) $180^\circ$

Question 11. The angle between the tangent at a point P on the circle and the radius through the point P is:

(A) $0^\circ$

(B) $45^\circ$

(C) $90^\circ$

(D) $180^\circ$

Question 12. A secant intersects a circle at how many points?

(A) Zero

(B) One

(C) Two

(D) Infinite

Question 13. If a line is perpendicular to the radius at its endpoint on the circle, then the line is a _____ to the circle at that point.

(A) Secant

(B) Chord

(C) Diameter

(D) Tangent

Question 14. From an external point P, tangents PA and PB are drawn to a circle with centre O. Then $\angle \text{APO}$ is equal to:

(A) $\angle \text{BPO}$

(B) $\angle \text{PAO}$

(C) $\angle \text{AOP}$

(D) $\angle \text{AOB}$

Question 15. From an external point P, tangents PA and PB are drawn to a circle with centre O. Then OP is the _____ of $\angle \text{APB}$.

(A) Altitude

(B) Median

(C) Angle bisector

(D) Perpendicular bisector

Question 16. If the angle between two tangents drawn from an external point P to a circle is $60^\circ$, and the radius of the circle is 10 cm, what is the distance from P to the centre O?

(A) 10 cm

(B) $10\sqrt{3}$ cm

(C) 20 cm

(D) $20\sqrt{3}$ cm

Question 17. A line is parallel to a tangent and a secant of a circle. The distance from the centre to the tangent is equal to the radius. The distance from the centre to the secant is:

(A) Equal to the radius

(B) Greater than the radius

(C) Less than the radius

(D) Equal to the diameter

Question 18. If two circles touch externally, the distance between their centres is equal to the:

(A) Sum of their radii

(B) Difference of their radii

(C) Product of their radii

(D) Ratio of their radii

Question 19. If two circles touch internally, the distance between their centres is equal to the:

(A) Sum of their radii

(B) Difference of their radii

(C) Product of their radii

(D) Ratio of their radii

Question 20. How many common tangents can be drawn to two disjoint circles?

(A) 1

(B) 2

(C) 3

(D) 4

Question 21. The angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment. This is known as the:

(A) Angle in a semicircle theorem

(B) Alternate Segment Theorem

(C) Tangent-Secant theorem

(D) Chord property

Question 1. A figure has line symmetry if it can be folded along a line so that the two halves:

(A) Are similar

(B) Overlap exactly

(C) Are parallel

(D) Are perpendicular

Question 2. The line along which a figure is folded to show line symmetry is called the:

(A) Centre of rotation

(B) Axis of symmetry

(C) Diagonal

(D) Base line

Question 3. Which of the following letters of the English alphabet has only horizontal line symmetry?

(A) A

(B) B

(C) O

(D) H

Question 4. How many lines of symmetry does a square have?

(A) 1

(B) 2

(C) 3

(D) 4

Question 5. How many lines of symmetry does an equilateral triangle have?

(A) 1

(B) 2

(C) 3

(D) 4

Question 6. A circle has how many lines of symmetry?

(A) 1

(B) 2

(C) A finite number

(D) An infinite number

Question 7. A reflection transformation is a type of:

(A) Dilation

(B) Rotation

(C) Translation

(D) Isometry (transformation that preserves distance)

Question 8. When a point $(x, y)$ is reflected across the x-axis, its new coordinates are:

(A) $(-x, y)$

(B) $(x, -y)$

(C) $(-x, -y)$

(D) $(y, x)$

Question 9. When a point $(x, y)$ is reflected across the y-axis, its new coordinates are:

(A) $(-x, y)$

(B) $(x, -y)$

(C) $(-x, -y)$

(D) $(y, x)$

Question 10. Which of the following geometric figures has no line symmetry?

(A) Isosceles triangle

(B) Rectangle

(C) Parallelogram (which is not a rhombus or rectangle)

(D) Rhombus

Question 11. How many lines of symmetry does a regular hexagon have?

(A) 3

(B) 4

(C) 6

(D) 8

Question 12. The reflection of a line segment across a line is a line segment that is _____ to the original line segment.

(A) Perpendicular

(B) Parallel

(C) Congruent

(D) Similar but not congruent

Question 13. Which of the following letters has both horizontal and vertical line symmetry?

(A) C

(B) E

(C) X

(D) T

Question 14. A figure is symmetric about a line if for every point on the figure, its reflection across the line is also:

(A) At the same distance from the line

(B) On the line

(C) On the figure itself

(D) At twice the distance from the line

Question 15. Which of the following shapes has exactly one line of symmetry?

(A) Square

(B) Rectangle

(C) Isosceles triangle (non-equilateral)

(D) Circle

Question 16. The reflection of a point across a line results in a point that is the same distance from the line as the original point, but on the _____ side of the line.

(A) Same

(B) Opposite

(C) Perpendicular

(D) Parallel

Question 17. How many lines of symmetry does a rhombus (which is not a square) have?

(A) 0

(B) 2

(C) 4

(D) Infinitely many

Question 18. The letter Z has:

(A) One vertical line of symmetry

(B) One horizontal line of symmetry

(C) No line symmetry

(D) Two lines of symmetry

Question 19. Reflection in geometry is essentially like looking at an image in a:

(A) Camera

(B) Magnifying glass

(C) Mirror

(D) Telescope

Question 20. If a point A is reflected across a line $l$ to get point A', then the line $l$ is the _____ of the segment AA'.

(A) Angle bisector

(B) Median

(C) Perpendicular bisector

(D) Altitude

Question 21. How many lines of symmetry does a regular pentagon have?

(A) 0

(B) 2

(C) 5

(D) 7

Question 22. A line segment has how many lines of symmetry?

(A) 0

(B) 1

(C) 2

(D) Infinite

Question 23. A scaling transformation changes the size of a figure but preserves its shape. Is scaling a type of reflectional symmetry?

(A) Yes

(B) No

(C) Sometimes

(D) Only if the scale factor is 1

Question 24. The image of a figure under reflection is _____ to the original figure.

(A) Similar only

(B) Congruent

(C) Neither similar nor congruent

(D) Twice the size

Question 1. A figure has rotational symmetry if it looks exactly the same after a rotation of less than a full turn ($360^\circ$) about a fixed point. This fixed point is called the:

(A) Axis of symmetry

(B) Centre of rotation

(C) Vertex

(D) Focus

Question 2. The smallest angle through which a figure can be rotated to match its original position is called the:

(A) Order of rotation

(B) Angle of rotational symmetry

(C) Centre of rotation

(D) Period of rotation

Question 3. The number of times a figure fits onto itself during a full rotation ($360^\circ$) is called the:

(A) Angle of rotation

(B) Centre of rotation

(C) Order of rotational symmetry

(D) Degree of rotation

Question 4. A square has rotational symmetry of order:

(A) 1

(B) 2

(C) 3

(D) 4

Question 5. What is the angle of rotational symmetry for a square?

(A) $90^\circ$

(B) $180^\circ$

(C) $270^\circ$

(D) $360^\circ$

Question 6. A rectangle (which is not a square) has rotational symmetry of order:

(A) 1

(B) 2

(C) 3

(D) 4

Question 7. The angle of rotational symmetry for a regular pentagon is:

(A) $60^\circ$

(B) $72^\circ$

(C) $90^\circ$

(D) $108^\circ$

Question 8. A circle has rotational symmetry of order:

(A) 1

(B) 2

(C) Finite

(D) Infinite

Question 9. The letter H has rotational symmetry of order:

(A) 1

(B) 2

(C) 3

(D) 4

Question 10. A figure has rotational symmetry of order 1 if:

(A) It has no rotational symmetry (other than the $360^\circ$ rotation)

(B) It is a regular polygon

(C) It has reflectional symmetry

(D) It can be rotated by $90^\circ$ to match itself

Question 11. Which of the following figures has rotational symmetry but NOT line symmetry?

(A) Square

(B) Equilateral triangle

(C) Parallelogram (which is not a rhombus or rectangle)

(D) Circle

Question 12. The angle of rotational symmetry is related to the order of rotational symmetry ($n$) by the formula:

(A) Angle = $n \times 360^\circ$

(B) Angle = $360^\circ + n$

(C) Angle = $360^\circ / n$

(D) Angle = $n / 360^\circ$

Question 13. A shape that looks the same after being rotated by $180^\circ$ about its centre has rotational symmetry of order:

(A) 1

(B) 2

(C) 3

(D) 4

Question 14. The centre of rotation for a regular polygon is usually its:

(A) Vertex

(B) Midpoint of a side

(C) Geometric centre (intersection of diagonals/medians/etc.)

(D) Any point inside the polygon

Question 15. Which of the following letters has rotational symmetry of order 2?

(A) A

(B) B

(C) C

(D) S

Question 16. A figure with rotational symmetry of order $n > 1$ will have $n$ angles of rotation that bring it back to its original position within a $360^\circ$ turn. The angles are multiples of the smallest angle of rotation. True or False?

(A) True

(B) False

(C) Only for even order

(D) Only for odd order

Question 17. How many degrees must a regular octagon (8 sides) be rotated about its centre to coincide with itself?

(A) $45^\circ$

(B) $90^\circ$

(C) $180^\circ$

(D) $360^\circ$

Question 18. A fan with 3 blades has rotational symmetry of order:

(A) 1

(B) 2

(C) 3

(D) 6

Question 19. The smallest angle of rotational symmetry for a fan with 3 blades is:

(A) $60^\circ$

(B) $90^\circ$

(C) $120^\circ$

(D) $180^\circ$

Question 20. A figure has no rotational symmetry (except for the $360^\circ$ rotation) if its order of rotational symmetry is:

(A) 0

(B) 1

(C) 2

(D) Infinite

Question 21. Which of the following figures always has rotational symmetry?

(A) Scalene triangle

(B) Parallelogram

(C) Trapezium

(D) Kite

Question 22. If a figure has rotational symmetry of order $n$, how many distinct positions does it take during a $360^\circ$ rotation (including the starting position)?

(A) $n-1$

(B) $n$

(C) $n+1$

(D) $360/n$

Question 1. 2-dimensional shapes can be drawn on a flat surface and have only length and breadth. 3-dimensional shapes have length, breadth, and:

(A) Area

(B) Perimeter

(C) Volume (or height/depth)

(D) Colour

Question 2. Which of the following is an example of a 2-dimensional shape?

(A) Cube

(B) Sphere

(C) Square

(D) Cylinder

Question 3. Which of the following is an example of a 3-dimensional shape?

(A) Triangle

(B) Circle

(C) Pentagon

(D) Cone

Question 4. The flat surfaces of a solid shape are called its:

(A) Edges

(B) Vertices

(C) Faces

(D) Boundaries

Question 5. The line segments where two faces of a solid shape meet are called its:

(A) Vertices

(B) Edges

(C) Faces

(D) Corners

Question 6. The points where three or more edges of a solid shape meet are called its:

(A) Faces

(B) Edges

(C) Vertices

(D) Corners

Question 7. A solid shape with six rectangular faces is called a:

(A) Cube

(B) Cylinder

(C) Cuboid

(D) Sphere

Question 8. A solid shape with six square faces is called a:

(A) Cuboid

(B) Prism

(C) Cube

(D) Pyramid

Question 9. A solid shape with a circular base and a curved surface tapering to a single point (vertex) is called a:

(A) Cylinder

(B) Sphere

(C) Cone

(D) Pyramid

Question 10. A solid shape with two circular bases and a curved surface joining them is called a:

(A) Cone

(B) Sphere

(C) Cylinder

(D) Prism

Question 11. A perfectly round solid shape where every point on the surface is equidistant from the centre is called a:

(A) Circle

(B) Hemisphere

(C) Sphere

(D) Disc

Question 12. A pyramid has a polygonal base and triangular faces that meet at a common vertex called the:

(A) Apex

(B) Base vertex

(C) Slant height

(D) Edge

Question 13. How many faces does a cuboid have?

(A) 4

(B) 6

(C) 8

(D) 12

Question 14. How many edges does a cube have?

(A) 6

(B) 8

(C) 12

(D) 18

Question 15. How many vertices does a cuboid have?

(A) 4

(B) 6

(C) 8

(D) 12

Question 16. A triangular prism has how many faces?

(A) 3

(B) 4

(C) 5

(D) 6

Question 17. Which of the following is NOT a face of a triangular prism?

(A) Triangle

(B) Square

(C) Rectangle

(D) All can be faces depending on the prism type

Question 18. A square pyramid has a square base. How many triangular faces does it have?

(A) 3

(B) 4

(C) 5

(D) 6

Question 19. A cylinder has how many plane faces?

(A) 0

(B) 1

(C) 2

(D) 3

Question 20. A cone has how many vertices?

(A) 0

(B) 1

(C) 2

(D) Infinite

Question 21. A sphere has how many edges and vertices?

(A) 1 edge, 1 vertex

(B) 0 edges, 0 vertices

(C) Infinite edges, infinite vertices

(D) 1 edge, 0 vertices

Question 22. A polyhedron is a solid figure whose faces are:

(A) Curved surfaces

(B) Polygons

(C) Circles

(D) Any closed shapes

Question 23. Which of the following is NOT a polyhedron?

(A) Cube

(B) Pyramid

(C) Prism

(D) Cylinder

Question 1. A sketch that gives a realistic impression of a 3D solid on a flat surface, where parallel lines remain parallel but angles are not preserved, is called a(n):

(A) Isometric sketch

(B) Orthographic projection

(C) Oblique sketch

(D) Net

Question 2. A sketch that represents a 3D solid on a flat surface by preserving actual measurements along the edges and angles (typically using a grid), is called a(n):

(A) Oblique sketch

(B) Orthographic projection

(C) Isometric sketch

(D) Cross-section

Question 3. Cutting a 3D solid with a plane gives a 2D shape called a:

(A) Net

(B) Surface

(C) Cross-section

(D) View

Question 4. If you slice a cube horizontally, the cross-section will be a:

(A) Triangle

(B) Circle

(C) Square

(D) Rectangle (unless the slice is through a vertex)

Question 5. If you slice a cylinder parallel to its base, the cross-section will be a:

(A) Square

(B) Rectangle

(C) Circle

(D) Ellipse

Question 6. The Front View, Side View, and Top View of a 3D object are examples of:

(A) Perspective drawings

(B) Oblique sketches

(C) Isometric sketches

(D) Orthographic projections

Question 7. When drawing a Top View of a solid, you are looking at the object from directly:

(A) In front

(B) From the side

(C) Above

(D) Below

Question 8. The cross-section of a cone sliced parallel to its base is a:

(A) Triangle

(B) Square

(C) Circle

(D) Trapezium

Question 9. If you slice a sphere with a plane, the cross-section is always a:

(A) Circle

(B) Ellipse

(C) Square

(D) Point

Question 10. An oblique sketch often starts with one face of the object drawn accurately in the plane of the paper. True or False?

(A) True

(B) False

(C) Depends on the object

(D) Only for cubes

Question 11. In an isometric sketch, the lines representing the three dimensions (length, width, height) originating from a point are drawn at angles of approximately:

(A) $90^\circ, 90^\circ, 90^\circ$

(B) $120^\circ, 120^\circ, 120^\circ$

(C) $45^\circ, 45^\circ, 90^\circ$

(D) $30^\circ, 30^\circ, 60^\circ$

Question 12. The shape of the base of a pyramid is a triangle. If you slice it parallel to the base, the cross-section will be a:

(A) Square

(B) Rectangle

(C) Triangle (similar to the base)

(D) Circle

Question 13. The shadows cast by 3D objects under a point source of light can be seen as a form of:

(A) Cross-section

(B) 2D representation

(C) Net

(D) Volume calculation

Question 14. Visualising the number of cubes needed to build a given shape is related to the concept of:

(A) Area

(B) Perimeter

(C) Volume

(D) Surface area

Question 15. A building blueprint usually contains multiple views (like floor plan, elevations). These views are examples of:

(A) Oblique sketches

(B) Isometric sketches

(C) Orthographic projections

(D) Perspective drawings

Question 16. If you slice a cube diagonally from one vertex to the opposite vertex, passing through the interior, the cross-section can be a:

(A) Triangle

(B) Rectangle

(C) Hexagon

(D) All of the above (depending on the angle and position of the slice)

Question 17. A net of a 3D shape is a 2D pattern that can be folded to form the solid. Is a net the same as a cross-section?

(A) Yes

(B) No

(C) Sometimes

(D) Only for cubes

Question 18. When drawing an oblique sketch, the lines perpendicular to the front face are often drawn at an angle (e.g., $45^\circ$) and their lengths may be:

(A) True length

(B) Half or two-thirds of the true length

(C) Doubled length

(D) Any arbitrary length

Question 19. The side view of a cuboid shows a:

(A) Point

(B) Line

(C) Rectangle (or square)

(D) Triangle

Question 20. If you slice a square pyramid vertically through its apex, the cross-section will be a:

(A) Square

(B) Rectangle

(C) Triangle

(D) Trapezium

Question 21. Visualizing a 3D solid by rotating it in your mind or using a model helps in understanding its:

(A) Area

(B) Volume

(C) Spatial properties and different views

(D) Centre of gravity

Question 1. A polyhedron is a solid figure bounded by plane faces. The faces of a polyhedron are:

(A) Circles

(B) Curved surfaces

(C) Polygons

(D) Any closed shapes

Question 2. A prism is a polyhedron with two identical and parallel bases and faces that are parallelograms. A triangular prism has bases that are:

(A) Squares

(B) Rectangles

(C) Triangles

(D) Pentagons

Question 3. A convex polyhedron is one where a line segment connecting any two points in the interior of the polyhedron lies entirely in the interior. Also, for every face, the polyhedron lies entirely on one side of the plane containing that face. True or False?

(A) True

(B) False

(C) Only true for Platonic solids

(D) Only true for prisms

Question 4. A regular polyhedron (Platonic solid) has faces made up of congruent regular polygons, and the same number of faces meet at each vertex. How many Platonic solids are there?

(A) 3

(B) 4

(C) 5

(D) 6

Question 5. The faces of a tetrahedron are:

(A) Squares

(B) Equilateral triangles

(C) Pentagons

(D) Hexagons

Question 6. The faces of a cube are:

(A) Triangles

(B) Squares

(C) Pentagons

(D) Hexagons

Question 7. Euler's formula for polyhedra relates the number of vertices (V), edges (E), and faces (F) of a convex polyhedron. The formula is:

(A) V + E + F = 2

(B) V - E + F = 2

(C) V + E - F = 2

(D) V - E - F = 2

Question 8. A cube has 8 vertices and 12 edges. Using Euler's formula, how many faces does it have?

(A) 4

(B) 6

(C) 8

(D) 10

Question 9. A triangular prism has 6 vertices and 9 edges. Using Euler's formula, how many faces does it have?

(A) 4

(B) 5

(C) 6

(D) 7

Question 10. Euler's formula V - E + F = 2 holds true for:

(A) All solid shapes

(B) All polyhedra

(C) All convex polyhedra

(D) Only Platonic solids

Question 11. Which of the following is a Platonic solid?

(A) Sphere

(B) Cylinder

(C) Icosahedron (20 faces)

(D) Pyramid

Question 12. A polyhedron whose faces are triangles is a:

(A) Prism

(B) Pyramid

(C) Dodecahedron

(D) Can be a prism or a pyramid

Question 13. The dual of a cube is an octahedron. If a cube has V=8, E=12, F=6, and an octahedron has V=6, E=12, F=8, do both satisfy Euler's formula?

(A) Only the cube satisfies it.

(B) Only the octahedron satisfies it.

(C) Neither satisfies it.

(D) Both satisfy it.

Question 14. A polyhedron has 7 faces and 15 edges. How many vertices does it have according to Euler's formula?

(A) 8

(B) 9

(C) 10

(D) 11

Question 15. A polyhedron has 10 vertices and 15 edges. How many faces does it have according to Euler's formula?

(A) 5

(B) 6

(C) 7

(D) 8

Question 16. The faces of a dodecahedron are:

(A) Triangles

(B) Squares

(C) Pentagons

(D) Hexagons

Question 17. A polyhedron with the minimum number of faces is a tetrahedron. How many faces does it have?

(A) 3

(B) 4

(C) 5

(D) 6

Question 18. Can a polyhedron have 10 vertices, 20 edges, and 10 faces?

(A) Yes

(B) No (Check with Euler's formula)

(C) Only if it is concave

(D) Only if it is a prism

Question 19. A prism with an n-sided polygonal base has (n+2) faces, 2n vertices, and 3n edges. Does this satisfy Euler's formula V - E + F = 2?

(A) Yes

(B) No

(C) Only for n=3

(D) Only for n=4

Question 20. A pyramid with an n-sided polygonal base has (n+1) faces, (n+1) vertices, and 2n edges. Does this satisfy Euler's formula V - E + F = 2?

(A) Yes

(B) No

(C) Only for n=3

(D) Only for n=4

Question 21. Which of the following is NOT a Platonic solid?

(A) Octahedron (8 faces)

(B) Hexahedron (Cube - 6 faces)

(C) Rhombic dodecahedron (12 faces, not regular)

(D) Icosahedron (20 faces)

Question 22. The faces of an octahedron are:

(A) Squares

(B) Equilateral triangles

(C) Pentagons

(D) Hexagons