Negative Questions MCQs for Sub-Topics of Topic 4: Geometry

Question 1. Which of the following is NOT a characteristic of a point in geometry?

(A) It represents a location.

(B) It has no dimension.

(C) It has a definite size.

(D) It is usually represented by a capital letter.

Question 2. Which of the following is NOT true about a geometric line?

(A) It extends infinitely in one direction.

(B) It has no breadth or thickness.

(C) It is determined by two distinct points.

(D) It extends infinitely in both directions.

Question 3. Which of the following is NOT a type of line relationship in a plane?

(A) Parallel lines

(B) Intersecting lines

(C) Curved lines

(D) Coincident lines

Question 4. Which of the following is NOT a characteristic of a plane?

(A) It is a flat surface.

(B) It has three dimensions.

(C) It extends infinitely.

(D) Three non-collinear points define a unique plane.

Question 5. Which of the following geometric elements does NOT have a definite length?

(A) Line segment

(B) Line

(C) Ray

(D) Both (B) and (C)

Question 6. Which of the following is NOT true about a ray AB (starting at A and passing through B)?

(A) It has one endpoint.

(B) It extends infinitely in the direction of B.

(C) It has a definite length.

(D) It is denoted by $\overrightarrow{AB}$.

Question 7. Which of the following is NOT an example of a line segment?

(A) An edge of a ruler.

(B) A stretched wire between two poles.

(C) The path of a projectile.

(D) The side of a triangle.

Question 8. Which of the following is NOT a closed curve?

(A) A circle.

(B) A square boundary.

(C) The letter 'C'.

(D) The boundary of a heart shape.

Question 9. Which of the following is NOT an undefined term in basic Euclidean geometry?

(A) Point

(B) Angle

(C) Line

(D) Plane

Question 10. If two lines in a plane are not parallel, which of the following is NOT true?

(A) They must intersect at exactly one point.

(B) They are intersecting lines.

(C) They are skew lines.

(D) They lie in the same plane.

Question 1. Which of the following is NOT a standard unit for measuring length?

(A) Metre

(B) Kilogram

(C) Centimetre

(D) Millimetre

Question 2. Which of the following tools is NOT primarily used for measuring angles?

(A) Protractor

(B) Set square (can be used to check specific angles)

(C) Ruler

(D) Clinometer

Question 3. Which of the following is NOT a component of an angle?

(A) Vertex

(B) Arms

(C) Degree

(D) Interior

Question 4. Which of the following statements about measuring line segments is NOT true?

(A) We compare the numerical lengths.

(B) A compass can be used to compare lengths.

(C) Visual estimation is always an accurate way to compare lengths.

(D) A ruler provides a scale for measurement.

Question 5. Which of the following points is NOT in the interior of $\angle \text{PQR}$?

(A) A point on the ray QP.

(B) A point between the rays QP and QR.

(C) The vertex Q.

(D) Both (A) and (C).

Question 6. Which of the following angle measures is NOT typically used in basic geometry?

(A) Degree ($\circ$)

(B) Radian

(C) Gradian

(D) All of the above are used.

Question 7. Which statement is NOT true about the measure of an angle?

(A) It is independent of the length of the arms.

(B) It is independent of the position of the vertex.

(C) It represents the amount of rotation between the arms.

(D) It is always a positive value.

Question 8. Which of the following is NOT a way to measure the length of a line segment AB?

(A) Place a ruler with 0 at A and read the value at B.

(B) Use a compass to transfer the length to a marked ruler.

(C) Count the number of unit squares it covers on a grid.

(D) Use a protractor.

Question 9. Which angle measure is NOT equal to $180^\circ$?

(A) A straight angle.

(B) The sum of angles in a triangle.

(C) Half of a complete angle.

(D) The sum of angles in a linear pair.

Question 10. If we say two line segments are congruent ($\cong$), what are we NOT saying about them?

(A) They have the same length.

(B) They can be made to coincide.

(C) They are parallel.

(D) They are equal in measure.

Question 1. Which of the following is NOT a recognized type of angle based on its measure?

(A) Acute angle

(B) Obtuse angle

(C) Curved angle

(D) Reflex angle

Question 2. Which statement is NOT true about a right angle?

(A) It measures $90^\circ$.

(B) It is greater than an obtuse angle.

(C) It is half of a straight angle.

(D) It is a quarter of a complete angle.

Question 3. Which of the following angle measures does NOT represent an obtuse angle?

(A) $91^\circ$

(B) $179^\circ$

(C) $180^\circ$

(D) $120^\circ$

Question 4. Which statement is NOT true about perpendicular lines?

(A) They intersect at $90^\circ$.

(B) They are parallel to each other.

(C) They form four right angles at their intersection.

(D) The symbol for perpendicularity is $\perp$.

Question 5. Which of the following is NOT true about a perpendicular bisector of a line segment?

(A) It is perpendicular to the segment.

(B) It passes through one of the endpoints of the segment.

(C) It passes through the midpoint of the segment.

(D) It contains all points equidistant from the segment's endpoints.

Question 6. If an angle is acute, which of the following is NOT true about its measure?

(A) It is less than $90^\circ$.

(B) It is greater than $0^\circ$.

(C) It is equal to $90^\circ$.

(D) It is less than a right angle.

Question 7. Which angle measure is NOT a reflex angle?

(A) $180^\circ$

(B) $200^\circ$

(C) $300^\circ$

(D) $359^\circ$

Question 8. If two lines are perpendicular, which statement is NOT necessarily true?

(A) They intersect.

(B) They form $90^\circ$ angles.

(C) They are in the same plane.

(D) They are concurrent at more than one point.

Question 9. Which of the following can NOT be a straight angle?

(A) The sum of angles in a linear pair.

(B) The angle formed by rotating $180^\circ$.

(C) An angle with measure $180^\circ$.

(D) The angle formed at the corner of a square.

Question 10. Which of the following is NOT a property of a zero angle?

(A) Its measure is $0^\circ$.

(B) Its arms coincide.

(C) It represents zero rotation.

(D) Its interior contains points.

Question 1. If two angles are complementary, which of the following is NOT necessarily true?

(A) Their sum is $90^\circ$.

(B) They are both acute angles.

(C) They are adjacent angles.

(D) They could be $30^\circ$ and $60^\circ$.

Question 2. If two angles are supplementary, which of the following is NOT necessarily true?

(A) Their sum is $180^\circ$.

(B) They form a linear pair.

(C) One angle is acute and the other is obtuse (unless both are $90^\circ$).

(D) They could be $70^\circ$ and $110^\circ$.

Question 3. Which of the following is NOT a condition for two angles to be adjacent?

(A) They share a common vertex.

(B) They share a common arm.

(C) Their non-common arms are on the same side of the common arm.

(D) They have no interior points in common.

Question 4. Which of the following is NOT true about a linear pair of angles?

(A) They are adjacent.

(B) Their non-common arms form a straight line.

(C) They are complementary.

(D) They are supplementary.

Question 5. Which of the following is NOT true about vertically opposite angles?

(A) They are formed by two intersecting lines.

(B) They are adjacent angles.

(C) They are always equal in measure.

(D) They share a common vertex.

Question 6. If two angles are supplementary and one is acute, which of the following is NOT true about the other angle?

(A) It is obtuse.

(B) It is a right angle.

(C) Its measure is greater than $90^\circ$.

(D) It forms a linear pair with the first angle (if adjacent).

Question 7. Which of the following pairs of angles are NOT necessarily equal?

(A) Two right angles.

(B) Two angles in a linear pair.

(C) Two vertically opposite angles.

(D) Two angles that are complements of the same angle.

Question 8. If $\angle A$ and $\angle B$ are complementary, and $\angle A = 30^\circ$, what is NOT true about $\angle B$?

(A) $\angle B = 60^\circ$.

(B) $\angle B$ is acute.

(C) $\angle B$ is obtuse.

(D) $\angle A + \angle B = 90^\circ$.

Question 9. Which property is NOT associated with angles formed by intersecting lines?

(A) Adjacent angles form linear pairs.

(B) Vertically opposite angles are equal.

(C) The sum of angles around the intersection point is $360^\circ$.

(D) Alternate interior angles are equal.

Question 10. If two angles are adjacent and their sum is $180^\circ$, which of the following is NOT true?

(A) They form a linear pair.

(B) They are supplementary.

(C) Their non-common arms form a straight line.

(D) They are complementary.

Question 1. Which of the following is NOT a type of angle pair formed when a transversal intersects two lines?

(A) Corresponding angles

(B) Alternate interior angles

(C) Adjacent angles

(D) Angle bisector angles

Question 2. Which of the following is NOT a property of angles formed when a transversal intersects two PARALLEL lines?

(A) Corresponding angles are equal.

(B) Alternate interior angles are supplementary.

(C) Consecutive interior angles are supplementary.

(D) Alternate exterior angles are equal.

Question 3. If a transversal intersects two lines such that alternate interior angles are equal, which of the following is NOT necessarily true?

(A) The two lines are parallel.

(B) Corresponding angles are equal.

(C) Consecutive interior angles are supplementary.

(D) The transversal is perpendicular to the two lines.

Question 4. Which of the following is NOT a criterion for proving that two lines are parallel when intersected by a transversal?

(A) A pair of corresponding angles are equal.

(B) A pair of alternate interior angles are equal.

(C) A pair of consecutive interior angles are complementary.

(D) A pair of consecutive interior angles are supplementary.

Question 5. If two lines are not parallel, which statement about the angles formed by a transversal is NOT true?

(A) Corresponding angles are not equal.

(B) Alternate interior angles are not equal.

(C) Consecutive interior angles are supplementary.

(D) The transversal intersects both lines.

Question 6. Which of the following is NOT a consequence of two lines being parallel and intersected by a transversal?

(A) All acute angles formed are equal.

(B) All obtuse angles formed are equal.

(C) Any acute angle and any obtuse angle formed are complementary.

(D) An acute angle and an obtuse angle on the same side of the transversal are supplementary.

Question 7. If a transversal intersects two lines such that consecutive interior angles are NOT supplementary, then:

(A) The lines are parallel.

(B) The lines are not parallel.

(C) Alternate interior angles are not equal.

(D) Corresponding angles are not equal.

Question 8. If line $p$ is parallel to line $q$, and line $r$ is a transversal, which angle pair is NOT necessarily supplementary?

(A) Interior angles on the same side.

(B) Consecutive interior angles.

(C) Corresponding angles.

(D) A linear pair formed by $r$ and $p$ (or $r$ and $q$).

Question 9. When two lines are intersected by a transversal, which angle pair is NOT always equal?

(A) Vertically opposite angles.

(B) Corresponding angles.

(C) Alternate interior angles.

(D) Alternate exterior angles.

Question 10. Which statement is NOT implied if corresponding angles formed by a transversal are equal?

(A) The two lines are parallel.

(B) Alternate interior angles are equal.

(C) Consecutive interior angles sum to $180^\circ$.

(D) The transversal is perpendicular to the lines.

Question 1. Which of the following is NOT a fundamental building block of the Euclidean geometry system?

(A) Undefined terms

(B) Definitions

(C) Conjectures

(D) Axioms and Postulates

Question 2. Which of the following statements is NOT an axiom or postulate assumed to be true in Euclidean geometry?

(A) A straight line can be drawn between any two points.

(B) All right angles are equal.

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

(D) Things equal to the same thing are equal to one another.

Question 3. Which of the following is NOT considered an undefined term in Euclidean geometry?

(A) Line segment

(B) Point

(C) Line

(D) Plane

Question 4. Which of the following is NOT true about a theorem in Euclidean geometry?

(A) It is a statement that is proven to be true.

(B) Its proof relies on definitions, axioms, and postulates.

(C) It is assumed to be true without proof.

(D) It is a logical consequence of the foundational statements.

Question 5. Which of the following is NOT a statement equivalent to Euclid's Fifth Postulate?

(A) Through a point not on a given line, there is exactly one line parallel to the given line.

(B) The sum of interior angles on the same side of a transversal intersecting two parallel lines is $180^\circ$.

(C) The area of a square on the hypotenuse of a right triangle is equal to the sum of the areas of the squares on the other two sides.

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

Question 6. Which of the following is NOT true about axioms (Common Notions)?

(A) They are assumed to be true.

(B) They are general statements, not limited to geometry.

(C) They need rigorous proof.

(D) An example is "The whole is greater than the part."

Question 7. Which of the following is NOT a postulate from Euclid's Elements?

(A) To draw a circle with any centre and radius.

(B) If equals be added to equals, the wholes are equal.

(C) To produce a terminated line indefinitely.

(D) All right angles are equal.

Question 8. Which statement is NOT true regarding the plane in Euclidean geometry?

(A) It has two dimensions.

(B) It has a definite boundary.

(C) Three non-collinear points define a unique plane.

(D) If two distinct lines intersect, they lie in the same plane.

Question 9. Which of the following can NOT be used as a justification step in a formal Euclidean geometry proof?

(A) Definition of perpendicular lines.

(B) Euclid's first postulate.

(C) An unproven conjecture.

(D) A previously proven theorem.

Question 10. Non-Euclidean geometries were developed by negating or modifying which specific part of Euclidean geometry's foundation?

(A) The definition of a point.

(B) The equality of right angles.

(C) Euclid's first four postulates.

(D) Euclid's Fifth Postulate.

Question 1. Which of the following is NOT a characteristic of a polygon?

(A) It is a simple closed curve.

(B) It is made up of only curved segments.

(C) Its sides are line segments.

(D) The segments intersect only at endpoints.

Question 2. Which of the following is NOT a term related to polygons?

(A) Side

(B) Vertex

(C) Focus

(D) Diagonal

Question 3. Which of the following is NOT a classification of polygons based on the number of sides?

(A) Triangle

(B) Circle

(C) Quadrilateral

(D) Pentagon

Question 4. Which of the following is NOT a type of polygon based on its shape properties?

(A) Convex polygon

(B) Curved polygon

(C) Regular polygon

(D) Irregular polygon

Question 5. Which statement is NOT true about a convex polygon?

(A) All its interior angles are less than $180^\circ$.

(B) All its diagonals lie entirely inside the polygon.

(C) At least one interior angle is greater than $180^\circ$.

(D) A line segment joining any two points in the interior lies entirely in the interior.

Question 6. Which statement is NOT true about a regular polygon?

(A) All its sides are equal.

(B) All its interior angles are equal.

(C) It is always a concave polygon.

(D) A square is a regular polygon.

Question 7. Which of the following is NOT a consequence of a polygon having $n$ sides?

(A) It has $n$ vertices.

(B) It has $n$ interior angles.

(C) The sum of its exterior angles is $n \times 360^\circ$.

(D) The sum of its interior angles is $(n-2) \times 180^\circ$.

Question 8. Which polygon type is NOT based on angle properties?

(A) Equiangular polygon.

(B) Acute-angled polygon.

(C) Obtuse-angled polygon.

(D) Equilateral polygon.

Question 9. Which of the following shapes is NOT a polygon?

(A) A triangle.

(B) A square.

(C) A shape made of 5 straight lines that do not form a closed region.

(D) A simple closed shape made of 6 line segments.

Question 10. Which statement about diagonals of a polygon is NOT true?

(A) They connect two non-adjacent vertices.

(B) They are always inside a convex polygon.

(C) A triangle has 3 diagonals.

(D) The number of diagonals in an n-sided polygon is $\frac{n(n-3)}{2}$.

Question 1. Which of the following is NOT a basic element of a triangle?

(A) Side

(B) Vertex

(C) Diagonal

(D) Angle

Question 2. Which of the following is NOT a classification of triangles based on sides?

(A) Scalene

(B) Isosceles

(C) Equilateral

(D) Right-angled

Question 3. Which of the following is NOT a classification of triangles based on angles?

(A) Acute-angled

(B) Obtuse-angled

(C) Straight-angled

(D) Right-angled

Question 4. Which statement is NOT true about an isosceles triangle?

(A) It has two equal sides.

(B) It has two equal angles.

(C) All three sides are equal.

(D) The angles opposite the equal sides are equal.

Question 5. Which of the following angle combinations can NOT form a triangle?

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

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

(C) $100^\circ, 40^\circ, 40^\circ$

(D) $90^\circ, 90^\circ, 0^\circ$

Question 6. Which statement is NOT true about a scalene triangle?

(A) All its sides are equal.

(B) All its sides are of different lengths.

(C) All its angles are of different measures.

(D) It is a type of triangle based on side lengths.

Question 7. Which statement is NOT true about a right-angled triangle?

(A) It has one angle that is exactly $90^\circ$.

(B) The other two angles are complementary.

(C) It can have an obtuse angle.

(D) The side opposite the right angle is the hypotenuse.

Question 8. Which type of triangle can NOT have an obtuse angle?

(A) Scalene

(B) Isosceles

(C) Equilateral

(D) Right-angled

Question 9. Which of the following is NOT a property of an equilateral triangle?

(A) All sides are equal.

(B) All angles are equal.

(C) Each angle measures $60^\circ$.

(D) It can have a right angle.

Question 10. Which statement is NOT true about classifying triangles?

(A) Triangles can be classified by their side lengths.

(B) Triangles can be classified by their angle measures.

(C) A triangle can only belong to one type of classification (e.g., if it's scalene, it can't be right-angled).

(D) Equilateral triangles are a subset of isosceles triangles.

Question 1. Which of the following is NOT true about the angles of a triangle?

(A) Their sum is $180^\circ$.

(B) Each exterior angle is equal to the sum of the two opposite interior angles.

(C) The sum of an interior angle and its adjacent exterior angle is $90^\circ$.

(D) The smallest angle is opposite the smallest side.

Question 2. In $\triangle$ABC, which statement is NOT true based on the Triangle Inequality Theorem?

(A) AB + BC > AC.

(B) AB + AC > BC.

(C) BC + AC > AB.

(D) AB + BC = AC.

Question 3. If in $\triangle$PQR, PQ > QR, which statement is NOT necessarily true about the angles?

(A) $\angle R > \angle P$.

(B) $\angle R < \angle P$.

(C) The angle opposite PQ is $\angle R$.

(D) The angle opposite QR is $\angle P$.

Question 4. Which of the following sets of lengths can NOT form a triangle?

(A) 3, 4, 5

(B) 6, 8, 10

(C) 2, 5, 7

(D) 7, 7, 7

Question 5. In an isosceles triangle with two equal sides, which statement is NOT true?

(A) The angles opposite the equal sides are equal.

(B) The third angle is equal to the equal angles.

(C) The sum of the two equal angles is less than $180^\circ$.

(D) It has at least one line of symmetry.

Question 6. If one angle of a triangle is obtuse, which of the following is NOT true about the other two angles?

(A) They are both acute.

(B) Their sum is less than $90^\circ$.

(C) Their sum is $180^\circ$ minus the obtuse angle.

(D) They are complementary.

Question 7. Which statement is NOT true about the exterior angle of a triangle?

(A) It is equal to the sum of the two opposite interior angles.

(B) It forms a linear pair with the adjacent interior angle.

(C) Its measure is less than the adjacent interior angle.

(D) It is greater than either of the two opposite interior angles.

Question 8. If two angles of a triangle are $30^\circ$ and $40^\circ$, which of the following is NOT true about the third angle?

(A) It measures $110^\circ$.

(B) It is an obtuse angle.

(C) It is an acute angle.

(D) The sum of the angles is $180^\circ$.

Question 9. Which statement is NOT true about the side-angle relationship in a triangle?

(A) The longest side is opposite the largest angle.

(B) The shortest side is opposite the smallest angle.

(C) If two angles are equal, the sides opposite them are unequal.

(D) If two sides are equal, the angles opposite them are equal.

Question 10. If the angles of a triangle are in the ratio 1:1:1, which statement is NOT true?

(A) It is an equilateral triangle.

(B) Each angle measures $60^\circ$.

(C) It is a right-angled triangle.

(D) It is an equiangular triangle.

Question 1. Which of the following is NOT a condition for applying the Pythagorean theorem?

(A) The triangle must be a right-angled triangle.

(B) You need to know the lengths of at least two sides.

(C) It can be used for any triangle.

(D) The sides are denoted as legs and a hypotenuse.

Question 2. If a right-angled triangle has legs of length $a$ and $b$ and hypotenuse of length $c$, which equation is NOT correct according to the Pythagorean theorem?

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

(B) $c = \sqrt{a^2 + b^2}$

(C) $a = \sqrt{c^2 - b^2}$

(D) $a + b = c$

Question 3. Which of the following sets of side lengths is NOT a Pythagorean triplet?

(A) (3, 4, 5)

(B) (5, 12, 13)

(C) (6, 8, 10)

(D) (4, 5, 6)

Question 4. If the sides of a triangle are $a, b, c$ and $a^2 + b^2 = c^2$, which statement is NOT true according to the converse of the Pythagorean theorem?

(A) The angle opposite side $c$ is a right angle.

(B) The triangle is a right-angled triangle.

(C) $c$ is the hypotenuse.

(D) The angle opposite side $a$ is obtuse.

Question 5. Which of the following is NOT an application of the Pythagorean theorem?

(A) Finding the diagonal of a square.

(B) Calculating the circumference of a circle.

(C) Finding the height of a ladder leaning against a wall.

(D) Calculating the distance between two points in a coordinate system.

Question 6. If the sides of a triangle are $a, b, c$ and $a^2 + b^2 < c^2$, which statement is NOT true?

(A) The angle opposite side $c$ is obtuse.

(B) The triangle is an obtuse-angled triangle.

(C) The angle opposite side $c$ is acute.

(D) This triangle is not a right triangle.

Question 7. In a right-angled triangle, if the hypotenuse is 17 units and one leg is 8 units, which statement is NOT true?

(A) The other leg is 15 units.

(B) $8^2 + 15^2 = 17^2$.

(C) The sides form a Pythagorean triplet.

(D) The other leg is 9 units.

Question 8. The Pythagorean theorem can be visually represented by the areas of squares built on the sides. Which statement is NOT part of this visual interpretation?

(A) The area of the square on the hypotenuse.

(B) The sum of the areas of the squares on the two legs.

(C) The perimeter of the squares.

(D) The equality between the area of the hypotenuse square and the sum of the areas of the leg squares.

Question 9. If a triangle has side lengths 2, 3, $\sqrt{13}$, which statement is NOT true?

(A) It is a right-angled triangle.

(B) $2^2 + 3^2 = 4 + 9 = 13$.

(C) $(\sqrt{13})^2 = 13$.

(D) The angle opposite the side of length 3 is $90^\circ$.

Question 10. Which of the following is NOT a necessary component of a right-angled triangle in the context of the Pythagorean theorem?

(A) Two legs.

(B) A hypotenuse.

(C) All angles are acute.

(D) One angle is $90^\circ$.

Question 1. Which of the following is NOT a condition for two geometric figures to be congruent?

(A) They have the same shape.

(B) They have the same size.

(C) They can be superimposed by rigid transformations.

(D) They have corresponding angles equal and corresponding sides proportional (ratio not necessarily 1:1).

Question 2. Which of the following statements about congruent line segments is NOT true?

(A) They have the same length.

(B) They are parallel.

(C) They are equal in measure.

(D) They can be made to coincide exactly.

Question 3. Which of the following is NOT a valid criterion for proving triangle congruence?

(A) SSS

(B) SAS

(C) AAA

(D) ASA

Question 4. If $\triangle \text{ABC} \cong \triangle \text{XYZ}$, which of the following statements is NOT necessarily true?

(A) $\angle A = \angle X$

(B) AB = XY

(C) BC = XZ

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

Question 5. Which statement about CPCTC is NOT true?

(A) It stands for Corresponding Parts of Congruent Triangles are Congruent.

(B) It is used to prove triangles are congruent.

(C) It is used after triangles have been proven congruent.

(D) It means that if two triangles are congruent, their corresponding sides and angles are equal.

Question 6. Which of the following pairs of figures are NOT necessarily congruent?

(A) Two circles with the same diameter.

(B) Two squares with the same perimeter.

(C) Two equilateral triangles with the same area.

(D) Two rectangles with the same area.

Question 7. Which statement is NOT true about the SAS congruence criterion?

(A) It requires two sides and the included angle of one triangle to be equal to the corresponding parts of the other.

(B) The angle must be between the two sides.

(C) It is a valid test for congruence.

(D) It is the same as the SSA criterion.

Question 8. If two triangles are congruent by the ASA criterion, which of the following is NOT one of the corresponding equal parts used in the criterion?

(A) Angle

(B) Included side

(C) Non-included side

(D) Angle

Question 9. Which statement is NOT true about the RHS congruence criterion?

(A) It applies to right-angled triangles.

(B) It requires the hypotenuse and one side to be equal to the corresponding parts.

(C) It is the same as the SSS criterion applied to right triangles.

(D) It is a valid test for congruence.

Question 10. If two angles are congruent, which statement is NOT true?

(A) Their measures are equal.

(B) They have the same vertex.

(C) They can be superimposed exactly.

(D) They are equal in measure.

Question 1. Which of the following is NOT a condition for two geometric figures to be similar?

(A) They have the same shape.

(B) They have the same size.

(C) Corresponding angles are equal.

(D) Corresponding sides are proportional.

Question 2. Which statement is NOT true about similar triangles?

(A) Corresponding angles are equal.

(B) Corresponding sides are equal.

(C) Corresponding sides are proportional.

(D) They have the same shape.

Question 3. Which of the following is NOT a valid criterion for proving triangle similarity?

(A) AA

(B) SSS (Proportionality)

(C) ASA

(D) SAS (Proportionality)

Question 4. Which statement is NOT true about the Basic Proportionality Theorem (BPT)?

(A) It deals with a line parallel to one side of a triangle.

(B) The parallel line must pass through the midpoint of one side.

(C) The parallel line intersects the other two sides at distinct points.

(D) It states that the other two sides are divided proportionally.

Question 5. If a line divides two sides of a triangle in the same ratio, which statement is NOT true according to the converse of the BPT?

(A) The line is parallel to the third side.

(B) The line is perpendicular to the third side.

(C) This property can be used to prove parallelism.

(D) This involves the ratio of segments of the sides.

Question 6. Which statement is NOT true about congruent figures vs similar figures?

(A) Congruent figures have the same shape and size.

(B) Similar figures have the same shape but can have different sizes.

(C) All congruent figures are similar.

(D) All similar figures are congruent.

Question 7. If $\triangle \text{ABC} \sim \triangle \text{PQR}$, which ratio is NOT necessarily equal to AB/PQ?

(A) AC/PR

(B) BC/QR

(C) Perimeter($\triangle \text{ABC}$)/Perimeter($\triangle \text{PQR}$)

(D) Area($\triangle \text{ABC}$)/Area($\triangle \text{PQR}$)

Question 8. Which of the following pairs of figures are NOT always similar?

(A) Two squares.

(B) Two circles.

(C) Two rectangles.

(D) Two equilateral triangles.

Question 9. If two triangles are similar by the SAS criterion, which statement is NOT true?

(A) One angle is equal to the corresponding angle.

(B) The sides including that angle are proportional.

(C) The ratio of the sides is 1:1.

(D) The corresponding angles are equal.

Question 10. Which statement is NOT true about the AA similarity criterion?

(A) It requires two pairs of corresponding angles to be equal.

(B) The third pair of angles is automatically equal.

(C) The corresponding sides are proportional.

(D) The corresponding sides are equal.

Question 1. If two triangles are similar, which statement about the ratio of their areas is NOT true?

(A) It is equal to the square of the ratio of corresponding sides.

(B) It is equal to the square of the ratio of corresponding altitudes.

(C) It is equal to the ratio of corresponding perimeters.

(D) It is equal to the square of the ratio of corresponding medians.

Question 2. If the ratio of corresponding sides of two similar triangles is 2:3, which statement is NOT true?

(A) The ratio of their perimeters is 2:3.

(B) The ratio of their altitudes is 2:3.

(C) The ratio of their areas is 4:9.

(D) The ratio of their angles is 2:3.

Question 3. The areas of two similar triangles are $64 \text{ cm}^2$ and $100 \text{ cm}^2$. Which statement about their corresponding sides is NOT true?

(A) The ratio of their areas is 64:100.

(B) The ratio of their areas simplifies to 16:25.

(C) The ratio of their corresponding sides is 8:10.

(D) The ratio of their corresponding sides is 64:100.

Question 4. In a right triangle ABC, right-angled at B, BD is the altitude to the hypotenuse AC. Which similarity relationship is NOT always 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) $\triangle \text{ADB} \cong \triangle \text{BDC}$

Question 5. Which of the following is NOT an application of similarity of triangles?

(A) Finding the height of a building using its shadow.

(B) Creating scale models of objects.

(C) Calculating the area of a square given its side.

(D) Determining the relationship between areas on maps and actual areas.

Question 6. If two similar triangles have perimeters in the ratio 5:7, which statement is NOT true?

(A) The ratio of corresponding sides is 5:7.

(B) The ratio of corresponding altitudes is 5:7.

(C) The ratio of their areas is 25:49.

(D) The ratio of their corresponding angles is 5:7.

Question 7. If the ratio of areas of two similar triangles is 1:1, which statement is NOT true?

(A) The triangles are congruent.

(B) The ratio of corresponding sides is 1:1.

(C) The triangles are only similar, not congruent.

(D) The ratio of corresponding perimeters is 1:1.

Question 8. In right triangle ABC, right-angled at B, BD is the altitude to AC. If AD = 3 and DC = 12, which statement is NOT true?

(A) BD = 6 (since $BD^2 = AD \times DC = 3 \times 12 = 36$).

(B) AB = $\sqrt{AD^2 + BD^2} = \sqrt{3^2 + 6^2} = \sqrt{9+36} = \sqrt{45}$.

(C) BC = $\sqrt{DC^2 + BD^2} = \sqrt{12^2 + 6^2} = \sqrt{144+36} = \sqrt{180}$.

(D) AC = AB + BC = $\sqrt{45} + \sqrt{180}$.

Question 9. If $\triangle \text{PQR} \sim \triangle \text{XYZ}$ and PQ/XY = 4/3, and Area($\triangle \text{XYZ}$) = $18 \text{ cm}^2$, which statement is NOT true?

(A) Area($\triangle \text{PQR}$)/Area($\triangle \text{XYZ}$) = $(4/3)^2 = 16/9$.

(B) Area($\triangle \text{PQR}$) = $(16/9) \times 18 = 16 \times 2 = 32 \text{ cm}^2$.

(C) The ratio of perimeters is 4:3.

(D) The ratio of corresponding angles is 4:3.

Question 10. Which of the following statements about similarity and area is NOT correct?

(A) If two triangles are similar, their areas are proportional to the square of their corresponding sides.

(B) If the areas of two triangles are proportional to the square of their corresponding sides, the triangles are similar.

(C) If two triangles have equal areas, they must be similar.

(D) If two triangles are congruent, they are similar and have equal areas.

Question 1. Which of the following is NOT a characteristic of a quadrilateral?

(A) It is a polygon.

(B) It has exactly 4 sides.

(C) It has exactly 3 vertices.

(D) It has 4 interior angles.

Question 2. Which statement is NOT true about the angles of a convex quadrilateral?

(A) The sum of the interior angles is $360^\circ$.

(B) Each interior angle is less than $180^\circ$.

(C) The sum of the exterior angles is $360^\circ$.

(D) All four interior angles are always equal.

Question 3. Which of the following is NOT a type of parallelogram?

(A) Rectangle

(B) Rhombus

(C) Trapezium

(D) Square

Question 4. Which statement is NOT true about the properties of a parallelogram?

(A) Opposite sides are parallel and equal.

(B) Opposite angles are equal.

(C) Adjacent angles are complementary.

(D) Diagonals bisect each other.

Question 5. Which statement is NOT true about the properties of a rectangle?

(A) It is a parallelogram.

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

(C) Diagonals are perpendicular.

(D) Diagonals are equal and bisect each other.

Question 6. Which statement is NOT true about the properties of a rhombus?

(A) It is a parallelogram.

(B) All four sides are equal.

(C) All four angles are $90^\circ$.

(D) Diagonals are perpendicular bisectors of each other.

Question 7. Which statement is NOT true about a square?

(A) It is a rectangle.

(B) It is a rhombus.

(C) Its diagonals are equal and perpendicular bisectors of each other.

(D) Its diagonals are not equal.

Question 8. Which statement is NOT true about a trapezium?

(A) It has at least one pair of parallel sides.

(B) Both pairs of opposite sides are parallel.

(C) An isosceles trapezium has non-parallel sides equal.

(D) The sum of interior angles is $360^\circ$.

Question 9. Which statement is NOT true about a kite?

(A) Two pairs of adjacent sides are equal.

(B) Opposite sides are parallel.

(C) The diagonals are perpendicular.

(D) One diagonal is the perpendicular bisector of the other.

Question 10. If the diagonals of a quadrilateral are equal and bisect each other, which statement is NOT true about the quadrilateral?

(A) It is a parallelogram.

(B) It is a rectangle.

(C) It is a rhombus.

(D) It has four right angles.

Question 1. Which statement is NOT part of the Mid-Point Theorem?

(A) The line segment joining the midpoints of two sides of a triangle is parallel to the third side.

(B) The line segment joining the midpoints of two sides of a triangle is equal to the third side.

(C) The line segment joining the midpoints of two sides of a triangle is half the length of the third side.

(D) It applies to triangles.

Question 2. Which statement is NOT true about the converse of the Mid-Point Theorem?

(A) A line is drawn through the midpoint of one side of a triangle.

(B) The line is perpendicular to another side.

(C) The line is parallel to another side.

(D) The line intersects the third side at its midpoint.

Question 3. In $\triangle$ABC, D is the midpoint of AB and E is the midpoint of AC. Which statement is NOT true?

(A) DE || BC.

(B) DE = $\frac{1}{2}$ BC.

(C) $\triangle \text{ADE}$ is congruent to $\triangle \text{ABC}$.

(D) $\triangle \text{ADE}$ is similar to $\triangle \text{ABC}$.

Question 4. Which of the following is NOT an application or consequence of the Mid-Point Theorem?

(A) Proving that the figure formed by joining the midpoints of a quadrilateral is a parallelogram.

(B) Proving that a line through a midpoint parallel to a side bisects the third side.

(C) Calculating the height of a triangle.

(D) Relating the perimeter of the triangle formed by midpoints to the original triangle's perimeter.

Question 5. In $\triangle$LMN, P, Q, R are the midpoints of LM, MN, NL respectively. If the area of $\triangle$LMN is $40 \text{ cm}^2$, which statement is NOT true?

(A) Area($\triangle \text{PQR}$) = $\frac{1}{4}$ Area($\triangle \text{LMN}$).

(B) Area($\triangle \text{PQR}$) = $10 \text{ cm}^2$.

(C) Area(quadrilateral LMPR) = $20 \text{ cm}^2$.

(D) The four smaller triangles ($\triangle \text{LPR}, \triangle \text{PMQ}, \triangle \text{QRN}, \triangle \text{PQR}$) have equal areas.

Question 6. If the figure formed by joining the midpoints of a quadrilateral is a rectangle, which statement about the original quadrilateral's diagonals is NOT true?

(A) They are equal.

(B) They are perpendicular.

(C) They bisect each other.

(D) They are perpendicular bisectors of each other.

Question 7. Which property is NOT directly part of the statement of the Mid-Point Theorem?

(A) Parallelism to the third side.

(B) Length being half of the third side.

(C) Dividing the third side into two equal parts.

(D) Joining the midpoints of two sides.

Question 8. If in $\triangle$XYZ, A is the midpoint of XY, and AB is drawn parallel to YZ, intersecting XZ at B, which statement is NOT true?

(A) B is the midpoint of XZ.

(B) AB = $\frac{1}{2}$ YZ.

(C) $\frac{XA}{AY} = \frac{XB}{BZ}$.

(D) $\triangle \text{XAB} \sim \triangle \text{XYZ}$.

Question 9. Which statement is NOT true about the relationship between the Mid-Point Theorem and the Basic Proportionality Theorem?

(A) MPT can be proven using BPT.

(B) BPT is a special case of MPT.

(C) Both involve lines parallel to a side of a triangle.

(D) MPT is a specific case of BPT where the ratio of division is 1:1.

Question 10. If the figure formed by joining the midpoints of a quadrilateral is a parallelogram, which statement is NOT necessarily true about the original quadrilateral?

(A) Its diagonals bisect each other.

(B) Its diagonals are equal.

(C) Its diagonals are perpendicular.

(D) It can be any quadrilateral.

Question 1. Which statement about the area of a plane figure is NOT true?

(A) It is the measure of the region enclosed by its boundary.

(B) It is a positive value for any non-empty region.

(C) It is measured in linear units.

(D) It is additive for non-overlapping regions.

Question 2. Which statement is NOT true about figures that are equal in area?

(A) They enclose the same amount of surface.

(B) They must be congruent.

(C) They might have different shapes.

(D) They might have different perimeters.

Question 3. Which statement is NOT true about parallelograms on the same base and between the same parallels?

(A) They have the same height.

(B) They have equal areas.

(C) They are congruent.

(D) The distance between the parallel lines is constant.

Question 4. Which statement is NOT true about triangles on the same base and between the same parallels?

(A) They have the same height.

(B) They have equal areas.

(C) They are congruent.

(D) Their third vertices lie on a line parallel to the base.

Question 5. If a triangle and a parallelogram are on the same base and between the same parallels, which statement is NOT true?

(A) The height of the triangle and parallelogram (relative to the base) are equal.

(B) The area of the triangle is twice the area of the parallelogram.

(C) The area of the triangle is half the area of the parallelogram.

(D) They share a common base segment.

Question 6. If two triangles have the same area and the same base, which statement is NOT true?

(A) Their heights are equal.

(B) They lie between the same parallels.

(C) They must be congruent.

(D) Their third vertices are equidistant from the base.

Question 7. In parallelogram ABCD, diagonal AC divides it into $\triangle$ABC and $\triangle$ADC. Which statement is NOT true?

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

(B) $\triangle \text{ABC}$ is congruent to $\triangle \text{ADC}$.

(C) $\triangle \text{ABC}$ and $\triangle \text{ADC}$ share the same base AC.

(D) Area($\triangle \text{ABC}$) + Area($\triangle \text{ADC}$) = Area(parallelogram ABCD).

Question 8. If a median is drawn in a triangle, which statement is NOT true about the two resulting triangles?

(A) They share the same vertex opposite the base.

(B) Their bases (on the side where the median is drawn) are equal.

(C) They are congruent.

(D) They have equal areas.

Question 9. Which statement is NOT true about the area of a figure after a rigid transformation (like translation or rotation)?

(A) The area remains the same.

(B) The shape remains the same.

(C) The size remains the same.

(D) The area changes proportionally to the transformation.

Question 10. Which statement is NOT true about measuring areas?

(A) Standard units like square metres are used.

(B) Area can be calculated using formulas based on side lengths and angles.

(C) Any two figures with the same perimeter must have the same area.

(D) The area of a complex shape can be found by dividing it into simpler shapes and summing their areas.

Question 1. Which of the following is NOT a basic term associated with a circle?

(A) Centre

(B) Vertex

(C) Radius

(D) Diameter

Question 2. Which statement about a chord of a circle is NOT true?

(A) It is a line segment joining two points on the circle.

(B) It always passes through the centre.

(C) The diameter is the longest chord.

(D) It divides the circle into segments.

Question 3. Which statement about the relationship between radius ($r$) and diameter ($d$) is NOT true?

(A) $d = 2r$

(B) $r = d/2$

(C) The diameter is twice the radius.

(D) The diameter is always greater than the circumference.

Question 4. Which of the following is NOT a part of a circle's boundary?

(A) Arc

(B) Circumference

(C) Radius

(D) Semicircle (as an arc)

Question 5. Which region of a circle is NOT bounded by two radii and an arc?

(A) Sector

(B) Quadrant (a sector with $90^\circ$ angle)

(C) Semicircle (a sector with $180^\circ$ angle)

(D) Segment

Question 6. If two circles are congruent, which statement is NOT true?

(A) They have the same radius.

(B) They have the same diameter.

(C) They have the same circumference.

(D) They have the same centre.

Question 7. Which statement about the interior and exterior of a circle is NOT true?

(A) A point in the interior has a distance from the centre less than the radius.

(B) A point in the exterior has a distance from the centre greater than the radius.

(C) A point on the boundary has a distance from the centre equal to the radius.

(D) The centre is in the exterior of the circle.

Question 8. Which statement is NOT true about arcs of a circle?

(A) They are parts of the circumference.

(B) A major arc is larger than the corresponding minor arc.

(C) An arc is a line segment.

(D) The sum of a major arc and its corresponding minor arc makes the full circle.

Question 9. Which statement is NOT true about the ratio $\pi$?

(A) It is the ratio of a circle's circumference to its diameter.

(B) It is approximately 3.14159.

(C) It is a rational number.

(D) It is a constant value for all circles.

Question 10. Which statement is NOT true about two similar circles?

(A) They have the same shape.

(B) Their radii are proportional (which is always true as they are just scaled versions).

(C) They have the same area.

(D) They can be of different sizes.

Question 1. Which statement is NOT true about the angle subtended by a chord at the centre compared to the angle subtended at a point on the circumference?

(A) The angle at the centre is twice the angle at the circumference.

(B) This applies to the angle subtended by the same arc.

(C) The angle at the circumference is half the angle at the centre.

(D) The angle at the centre is equal to the angle at the circumference.

Question 2. Which statement about equal chords of a circle is NOT true?

(A) They subtend equal angles at the centre.

(B) They are equidistant from the centre.

(C) They are always parallel.

(D) They subtend equal angles at the circumference.

Question 3. Which statement about the perpendicular from the centre of a circle to a chord is NOT true?

(A) It bisects the chord.

(B) It bisects the angle subtended by the chord at the centre.

(C) It is parallel to the chord.

(D) It is the shortest distance from the centre to the chord.

Question 4. Which statement about angles in the same segment of a circle is NOT true?

(A) They are equal.

(B) They are subtended by the same chord or arc.

(C) They are complementary.

(D) They lie in the same part of the circle relative to the chord.

Question 5. Which statement about the angle in a semicircle is NOT true?

(A) It is a right angle.

(B) It measures $90^\circ$.

(C) It is an acute angle.

(D) It is subtended by a diameter at a point on the circumference.

Question 6. If two chords subtend equal angles at the centre of a circle, which statement is NOT true?

(A) The chords are equal in length.

(B) The chords are equidistant from the centre.

(C) The chords are perpendicular.

(D) The arcs corresponding to the chords are congruent.

Question 7. Which statement is NOT true about a secant?

(A) It is a line.

(B) It intersects the circle at exactly one point.

(C) It contains a chord of the circle.

(D) It intersects the circle at two distinct points.

Question 8. If the angle subtended by a chord at the centre is $100^\circ$, which statement is NOT true?

(A) The angle subtended by the chord on the major arc is $50^\circ$.

(B) The reflex angle subtended by the chord at the centre is $260^\circ$.

(C) The angle subtended by the chord on the minor arc is $130^\circ$.

(D) The chord is a diameter.

Question 9. Which statement about the locus of points equidistant from two points on a circle's circumference is NOT true?

(A) The locus is a line.

(B) The line is perpendicular to the chord joining the two points.

(C) The line passes through the centre of the circle.

(D) The locus is a circle concentric with the original circle.

Question 10. Which statement about the segment of a circle is NOT true?

(A) It is the region between a chord and its corresponding arc.

(B) A diameter divides the circle into two major segments.

(C) It can be a major segment or a minor segment.

(D) The angle in a major segment is acute.

Question 1. Which statement is NOT true about a cyclic quadrilateral?

(A) All its vertices lie on a circle.

(B) The sum of opposite angles is $180^\circ$.

(C) The diagonals are always perpendicular bisectors of each other.

(D) The exterior angle at a vertex is equal to the interior opposite angle.

Question 2. If ABCD is a cyclic quadrilateral, which statement is NOT true?

(A) $\angle A + \angle C = 180^\circ$.

(B) $\angle B + \angle D = 180^\circ$.

(C) The sum of all four interior angles is $360^\circ$.

(D) Adjacent angles are always equal.

Question 3. Which of the following quadrilaterals is NOT always cyclic?

(A) Square

(B) Rectangle

(C) Rhombus

(D) Isosceles trapezium

Question 4. If a parallelogram is cyclic, which statement is NOT true?

(A) It must be a rectangle.

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

(C) Its diagonals are perpendicular.

(D) It could be a square.

Question 5. If a quadrilateral has opposite angles supplementary, which statement is NOT true?

(A) The quadrilateral is cyclic.

(B) All its vertices lie on a circle.

(C) It is necessarily a parallelogram.

(D) The exterior angle at a vertex equals the interior opposite angle.

Question 6. If ABCD is a cyclic quadrilateral and $\angle A = 60^\circ$, which statement is NOT true?

(A) $\angle C = 120^\circ$.

(B) $\angle A$ and $\angle C$ are supplementary.

(C) The exterior angle at A is $60^\circ$.

(D) $\angle B + \angle D = 180^\circ$.

Question 7. Which statement about an isosceles trapezium is NOT true?

(A) It has one pair of parallel sides.

(B) Its non-parallel sides are equal.

(C) Its diagonals bisect each other.

(D) It can be a cyclic quadrilateral.

Question 8. If four points are concyclic, which statement is NOT true?

(A) They lie on the same circle.

(B) Any quadrilateral formed by joining them in order is cyclic.

(C) They must form a regular polygon.

(D) They satisfy the condition that opposite angles of the resulting quadrilateral sum to $180^\circ$.

Question 9. If a cyclic quadrilateral has diagonals that are perpendicular, which statement is NOT necessarily true?

(A) The quadrilateral is a kite.

(B) The sums of products of opposite sides are equal (Ptolemy's Theorem applies to all cyclic quads).

(C) It is a square.

(D) It could be a rhombus (if it's a square).

Question 10. Which of the following is NOT a property of cyclic quadrilaterals?

(A) Opposite angles sum to $180^\circ$.

(B) Exterior angle equals interior opposite angle.

(C) All sides are equal.

(D) Vertices lie on a circle.

Question 1. Which statement is NOT true about a tangent to a circle?

(A) It is a line.

(B) It intersects the circle at two points.

(C) It intersects the circle at exactly one point.

(D) It is perpendicular to the radius at the point of contact.

Question 2. Which statement is NOT true about a secant to a circle?

(A) It is a line.

(B) It intersects the circle at two distinct points.

(C) The segment of the secant inside the circle is a chord.

(D) It touches the circle at exactly one point.

Question 3. Which statement about the number of tangents from a point is NOT true?

(A) From a point inside the circle, zero tangents can be drawn.

(B) From a point on the circle, one tangent can be drawn.

(C) From a point outside the circle, three tangents can be drawn.

(D) From a point outside the circle, two tangents can be drawn.

Question 4. If tangents PA and PB are drawn from an external point P to a circle, which statement is NOT true?

(A) PA = PB.

(B) $\triangle \text{PAB}$ is an isosceles triangle.

(C) The angles subtended by PA and PB at the centre are equal.

(D) The angle between PA and PB is always $90^\circ$.

Question 5. Which statement about parallel tangents is NOT true?

(A) At most two parallel tangents can be drawn to a circle.

(B) The line segment joining the points of contact of two parallel tangents is a diameter.

(C) Parallel tangents are equidistant from the centre.

(D) Parallel tangents can be drawn from the same external point.

Question 6. If a line is perpendicular to a radius at its endpoint on the circle, which statement is NOT true?

(A) The line is a tangent at that point.

(B) The line is the shortest distance from the centre to the line.

(C) The line passes through the centre.

(D) This is the converse of the Tangent-Radius theorem.

Question 7. If two circles touch externally, which statement is NOT true?

(A) The distance between their centres is the sum of their radii.

(B) They have a common tangent at the point of contact.

(C) They intersect at two distinct points.

(D) The point of contact lies on the line joining the centres.

Question 8. If two circles intersect at two distinct points, which statement is NOT true?

(A) The distance between their centres is less than the sum of their radii.

(B) The distance between their centres is greater than the difference of their radii.

(C) They have a common chord.

(D) They have a common tangent.

Question 9. Which statement is NOT true about the Alternate Segment Theorem?

(A) It relates the angle between a tangent and a chord to an angle in the alternate segment.

(B) The chord must pass through the point of contact.

(C) It applies to any chord in the circle.

(D) The angle in the alternate segment is equal to the angle between the tangent and chord.

Question 10. If tangents PA and PB are drawn from external point P to a circle with centre O, which statement is NOT always true?

(A) PO bisects $\angle APB$.

(B) PO bisects $\angle AOB$.

(C) $\angle PAO = 90^\circ$.

(D) $\angle AOB = \angle APB$.

Question 1. Which statement is NOT true about line symmetry?

(A) It is also called reflectional symmetry.

(B) The figure is its own image when reflected across the line of symmetry.

(C) The line of symmetry is parallel to the figure.

(D) The line of symmetry divides the figure into two congruent halves.

Question 2. Which of the following shapes does NOT have any line symmetry?

(A) Square

(B) Circle

(C) Scalene triangle

(D) Isosceles triangle (not equilateral)

Question 3. Which of the following letters of the English alphabet does NOT have any line symmetry?

(A) A

(B) S

(C) M

(D) O

Question 4. How many lines of symmetry does a rectangle that is NOT a square NOT have?

(A) 0

(B) 2

(C) More than 2

(D) 4

Question 5. Which statement about the reflection of a point (x, y) across a line is NOT true?

(A) Reflection across the x-axis maps (x, y) to (x, -y).

(B) Reflection across the y-axis maps (x, y) to (-x, y).

(C) Reflection across the origin maps (x, y) to (-x, -y).

(D) Reflection across the line y = x maps (x, y) to (-x, y).

Question 6. Which of the following shapes does NOT have exactly one line of symmetry?

(A) Isosceles triangle (not equilateral)

(B) Kite (not a rhombus)

(C) A semicircle (including the diameter)

(D) Rhombus (not a square)

Question 7. Which statement about reflection as a transformation is NOT true?

(A) It preserves distance.

(B) It preserves angle measures.

(C) It preserves orientation (e.g., clockwise order of vertices).

(D) It is an isometry.

Question 8. If a figure has line symmetry about a line $l$, and P is a point on the figure, which statement is NOT true?

(A) The reflection of P across $l$ is also on the figure.

(B) If P is not on $l$, then the line segment PP' (where P' is the reflection) is perpendicular to $l$.

(C) If P is not on $l$, then the distance from P to $l$ is equal to the distance from P' to $l$.

(D) If P is on $l$, its reflection P' is at twice the distance from $l$.

Question 9. Which of the following letters does NOT have horizontal line symmetry?

(A) C

(B) D

(C) A

(D) E

Question 10. Which statement about the lines of symmetry of a regular n-sided polygon is NOT true?

(A) It has n lines of symmetry.

(B) If n is odd, the lines of symmetry pass through vertices and midpoints of opposite sides.

(C) If n is even, the lines of symmetry pass through opposite vertices or midpoints of opposite sides.

(D) The lines of symmetry intersect at the midpoints of the sides.

Question 1. Which statement is NOT true about rotational symmetry?

(A) The figure coincides with its original position after a rotation less than $360^\circ$.

(B) The rotation is about a fixed point called the centre of rotation.

(C) The smallest such angle is the angle of rotational symmetry.

(D) It implies the figure also has line symmetry.

Question 2. Which figure does NOT have rotational symmetry of order greater than 1?

(A) Square

(B) Equilateral triangle

(C) Scalene triangle

(D) Circle

Question 3. Which statement is NOT true about the order of rotational symmetry ($n$)?

(A) It is the number of times a figure coincides with itself in $360^\circ$.

(B) It is related to the angle of rotational symmetry ($\theta$) by $n = 360^\circ / \theta$.

(C) If $n=1$, the figure has no rotational symmetry other than the $360^\circ$ turn.

(D) It can be any positive real number.

Question 4. Which of the following letters does NOT have rotational symmetry of order 2?

(A) H

(B) I

(C) X

(D) A

Question 5. If a regular polygon has an angle of rotational symmetry of $40^\circ$, which statement is NOT true?

(A) The order of rotational symmetry is $360/40 = 9$.

(B) The polygon has 9 sides.

(C) The sum of interior angles is $(9-2) \times 180^\circ = 7 \times 180^\circ = 1260^\circ$.

(D) Each interior angle is $40^\circ$.

Question 6. Which statement about the centre of rotation is NOT true?

(A) It is a fixed point.

(B) It must be inside the figure.

(C) The figure rotates around this point.

(D) For a regular polygon, it is the geometric centre.

Question 7. Which of the following shapes does NOT have both line symmetry and rotational symmetry (order > 1)?

(A) Square

(B) Equilateral triangle

(C) Circle

(D) Parallelogram (not rhombus/rectangle)

Question 8. Which statement is NOT true about a figure with rotational symmetry of order $n > 1$?

(A) It has at least one line of symmetry.

(B) It coincides with itself after rotations of $360^\circ/n, 2(360^\circ/n), ...$

(C) It takes $n$ distinct positions during a full $360^\circ$ rotation.

(D) Its angle of rotational symmetry is less than $360^\circ$.

Question 9. If a figure has rotational symmetry of order 3, which statement is NOT true?

(A) The angle of rotational symmetry is $120^\circ$.

(B) It coincides with itself after rotating by $120^\circ$ and $240^\circ$.

(C) It could be an equilateral triangle.

(D) It has exactly 3 lines of symmetry.

Question 10. Which of the following is NOT a property of rotational symmetry?

(A) It involves rotation around a fixed point.

(B) It preserves distance and angle measures.

(C) It involves reflection across a line.

(D) It can be described by an angle and an order.

Question 1. Which statement is NOT true about the difference between 2D and 3D shapes?

(A) 2D shapes have length and breadth.

(B) 3D shapes have length, breadth, and height.

(C) 2D shapes have volume, while 3D shapes have area.

(D) 2D shapes can be drawn on a flat surface, while 3D shapes cannot be fully represented without perspective or multiple views.

Question 2. Which of the following is NOT an example of a solid shape?

(A) Cube

(B) Circle

(C) Sphere

(D) Pyramid

Question 3. Which of the following is NOT a term used to describe parts of a solid shape?

(A) Face

(B) Edge

(C) Vertex

(D) Circumference

Question 4. Which statement about the faces of a solid shape is NOT true?

(A) Faces are the outer surfaces of the solid.

(B) Faces can be plane or curved.

(C) All solid shapes have only plane faces.

(D) The faces form the boundary of the solid.

Question 5. Which statement about the edges of a solid shape is NOT true?

(A) Edges are where two faces meet.

(B) Edges can be straight or curved.

(C) A sphere has straight edges.

(D) Edges form the boundaries of the faces.

Question 6. Which statement about the vertices of a solid shape is NOT true?

(A) Vertices are where edges meet.

(B) A vertex is usually a point or a corner.

(C) A cylinder has vertices.

(D) A cube has 8 vertices.

Question 7. Which statement about a cube is NOT true?

(A) It is a solid shape.

(B) All its faces are congruent squares.

(C) It has 6 vertices.

(D) It has 12 edges.

Question 8. Which statement about a cylinder is NOT true?

(A) It has two circular bases.

(B) It has a curved surface.

(C) It has 2 edges (curved).

(D) It has vertices.

Question 9. Which statement about a cone is NOT true?

(A) It has a circular base.

(B) It has a curved surface.

(C) It has two vertices.

(D) It tapers to an apex.

Question 10. Which statement about a sphere is NOT true?

(A) Every point on its surface is equidistant from the centre.

(B) It has edges.

(C) It has vertices.

(D) Both (B) and (C).

Question 1. Which of the following is NOT a method for representing a 3D solid on a flat surface?

(A) Oblique sketch

(B) Area calculation

(C) Isometric sketch

(D) Orthographic projection (Views)

Question 2. Which statement about a cross-section of a solid is NOT true?

(A) It is the 2D shape obtained by slicing the solid with a plane.

(B) It always results in a circular shape.

(C) It helps in visualizing the internal structure of the solid.

(D) Different slices can produce different cross-sections for the same solid.

Question 3. If you slice a cube, which of the following shapes can NOT be obtained as a cross-section?

(A) Square

(B) Circle

(C) Rectangle

(D) Triangle

Question 4. Which of the following is NOT a standard view used in orthographic projection?

(A) Front View

(B) Side View

(C) Diagonal View

(D) Top View

Question 5. Which statement is NOT true about an oblique sketch?

(A) The front face is typically drawn in its true shape and size.

(B) Lines representing depth are drawn at a receding angle.

(C) All angles and lengths are shown in their true measure.

(D) Parallel lines in the solid are represented as parallel lines in the sketch.

Question 6. Which statement is NOT true about an isometric sketch?

(A) It is drawn on an isometric grid.

(B) All edge lengths are drawn to scale (along the isometric axes).

(C) The front face is drawn in its true shape.

(D) Lines along the three visible axes appear at $120^\circ$ to each other.

Question 7. If you slice a cone parallel to its base, which shape is NOT obtained as a cross-section?

(A) Circle (if the slice is not through the vertex).

(B) Point (if the slice is through the vertex).

(C) Ellipse (if sliced at an angle not parallel to base or perpendicular to axis).

(D) Square.

Question 8. Which statement is NOT true about the different views (Front, Side, Top)?

(A) They show the object from different perpendicular directions.

(B) They preserve angle measures.

(C) They are a type of perspective drawing.

(D) They provide a complete set of information to reconstruct the solid (for simple objects).

Question 9. Which statement is NOT true about a net of a solid?

(A) It is a 2D pattern.

(B) It can be folded to form the 3D solid.

(C) Every solid has only one unique net.

(D) It shows the faces of the solid laid out flat.

Question 10. Which statement is NOT a common technique for visualizing 3D shapes?

(A) Looking at the object from different angles.

(B) Cutting cross-sections.

(C) Building a physical model.

(D) Calculating the surface area.

Question 1. Which of the following is NOT a polyhedron?

(A) Cube

(B) Pyramid

(C) Cone

(D) Prism

Question 2. Which statement is NOT true about the faces, edges, and vertices of a polyhedron?

(A) Faces are polygonal regions.

(B) Edges are where faces intersect.

(C) Vertices are where edges intersect.

(D) The number of faces is always equal to the number of vertices.

Question 3. Which statement is NOT true about a convex polyhedron?

(A) For any face, the rest of the polyhedron lies entirely on one side of the plane of that face.

(B) A line segment joining any two points in the interior lies entirely in the interior.

(C) It has at least one interior angle greater than $180^\circ$ (in terms of angles of faces).

(D) Cubes and pyramids are convex polyhedra.

Question 4. Which statement is NOT true about a regular polyhedron (Platonic solid)?

(A) Its faces are all congruent regular polygons.

(B) The same number of faces meet at each vertex.

(C) It can be any convex polyhedron.

(D) There are exactly 5 Platonic solids.

Question 5. Which statement is NOT true about Euler's formula (V - E + F = 2)?

(A) It relates the number of vertices, edges, and faces.

(B) It applies to all solid shapes.

(C) It applies to convex polyhedra.

(D) It can be used to find V, E, or F if the other two are known.

Question 6. A polyhedron has 7 vertices and 12 edges. Which statement is NOT true, assuming it is a convex polyhedron?

(A) Using V - E + F = 2, $7 - 12 + F = 2$.

(B) F = 2 + 12 - 7 = 7.

(C) The polyhedron has 7 faces.

(D) This must be a cube.

Question 7. Which statement is NOT true about the faces of the 5 Platonic solids?

(A) Tetrahedron faces are triangles.

(B) Cube faces are squares.

(C) Octahedron faces are squares.

(D) Dodecahedron faces are pentagons.

Question 8. If a solid has V=10, E=15, F=7, which statement is NOT true?

(A) V - E + F = $10 - 15 + 7 = 2$.

(B) This combination satisfies Euler's formula.

(C) This solid must be a cone.

(D) This solid could be a convex polyhedron.

Question 9. Which statement is NOT true about prisms and pyramids?

(A) Prisms have two identical parallel bases.

(B) Pyramids have one base and triangular faces meeting at an apex.

(C) Both are types of polyhedra.

(D) Both always have square bases.

Question 10. Which statement is NOT true about the dual relationship between Platonic solids?

(A) The dual of a cube is an octahedron.

(B) The number of vertices of a solid equals the number of faces of its dual.

(C) The number of edges is the same for a solid and its dual.

(D) The dual of a tetrahedron is a cube.