Completing Statements MCQs for Sub-Topics of Topic 5: Construction

Question 1. To construct a circle with a radius of $6 \text{ cm}$ using a compass, the distance between the sharp point and the pencil tip should be set to ______.

(A) $3 \text{ cm}$

(B) $6 \text{ cm}$

(C) $12 \text{ cm}$

(D) Any distance

Question 2. If the diameter of a circle is $18 \text{ cm}$, the radius used for construction is ______.

(A) $18 \text{ cm}$

(B) $36 \text{ cm}$

(C) $9 \text{ cm}$

(D) $4.5 \text{ cm}$

Question 3. A line segment is a part of a line that has ______ endpoints.

(A) One

(B) Two

(C) Infinite

(D) No

Question 4. To construct a line segment of a given length using a ruler, you typically start marking from the ______ mark on the ruler.

(A) $1 \text{ cm}$

(B) $0$

(C) Any

(D) $1 \text{ mm}$

Question 5. Copying a line segment AB onto a line L starting at point P using a compass involves setting the compass opening equal to the ______ of AB.

(A) Angle

(B) Length

(C) Midpoint

(D) Slope

Question 6. The fixed point around which a compass rotates to draw a circle is called the ______.

(A) Radius

(B) Diameter

(C) Circumference

(D) Centre

Question 7. A line segment has a definite ______.

(A) Position

(B) Angle

(C) Length

(D) Width

Question 8. All points on a circle are equidistant from the ______.

(A) Diameter

(B) Circumference

(C) Centre

(D) Any point on the circle

Question 9. To accurately construct a line segment of length $3.4 \text{ cm}$ using a ruler, you should look at the scale ______ to avoid parallax error.

(A) From the left

(B) From the right

(C) Perpendicularly

(D) At an angle

Question 10. When you copy a line segment using a compass, you are essentially transferring its ______.

(A) Position

(B) Length

(C) Orientation

(D) Colour

Question 11. A circle is defined by its centre and its ______.

(A) Area

(B) Circumference

(C) Radius

(D) Diameter

Question 12. The longest chord in a circle is the ______.

(A) Radius

(B) Diameter

(C) Secant

(D) Tangent

Question 1. To construct a $60^\circ$ angle using a compass and ruler, you draw an arc from the vertex and then a second arc from the intersection on the ray using the ______ radius.

(A) Double

(B) Half

(C) Same

(D) Any

Question 2. Bisecting a $90^\circ$ angle results in two angles of ______ degrees each.

(A) $30$

(B) $45$

(C) $60$

(D) $22.5$

Question 3. An angle bisector divides an angle into two ______ angles.

(A) Obtuse

(B) Complementary

(C) Supplementary

(D) Equal

Question 4. To construct a $90^\circ$ angle at a point on a line, you can bisect a ______ angle.

(A) $60^\circ$

(B) $120^\circ$

(C) $180^\circ$

(D) $270^\circ$

Question 5. The justification for angle bisector construction relies on the property that any point on the bisector is equidistant from the ______ of the angle.

(A) Vertex

(B) Arms

(C) Midpoint

(D) Endpoints

Question 6. To construct a $30^\circ$ angle, you first construct a $60^\circ$ angle and then ______ it.

(A) Double

(B) Triple

(C) Bisect

(D) Extend

Question 7. An angle of $75^\circ$ can be constructed by combining constructions for $60^\circ$ and ______ degrees.

(A) $15$

(B) $30$

(C) $45$

(D) $90$

Question 8. Which geometric tool is specifically designed for measuring or drawing angles?

(A) Ruler

(B) Compass

(C) Protractor

(D) Divider

Question 9. The justification of angle bisector construction often uses the ______ congruence criterion.

(A) ASA

(B) SAS

(C) SSS

(D) RHS

Question 10. An angle of $150^\circ$ can be constructed by combining constructions for $90^\circ$ and ______ degrees.

(A) $30$

(B) $45$

(C) $60$

(D) $75$

Question 1. A line perpendicular to another line makes an angle of ______ degrees with it.

(A) $45$

(B) $60$

(C) $90$

(D) $180$

Question 2. To construct a perpendicular to a line from a point on the line, you are essentially constructing a ______ angle at that point.

(A) $60^\circ$

(B) $90^\circ$

(C) $120^\circ$

(D) $180^\circ$

Question 3. The perpendicular bisector of a line segment passes through the ______ of the segment and is perpendicular to it.

(A) Endpoint

(B) Midpoint

(C) Vertex

(D) Center

Question 4. To construct the perpendicular bisector of a line segment AB, the radius of the arcs drawn from A and B must be greater than ______ the length of AB.

(A) Twice

(B) Equal to

(C) Half

(D) Quarter

Question 5. Any point on the perpendicular bisector of a line segment is ______ from the endpoints of the segment.

(A) Closer

(B) Further

(C) Equidistant

(D) Twice the distance

Question 6. The shortest distance from a point to a line is measured along the ______ segment from the point to the line.

(A) Parallel

(B) Perpendicular

(C) Horizontal

(D) Longest

Question 7. To construct a perpendicular to a line from a point outside the line, you first draw an arc from the point intersecting the line at ______ points.

(A) One

(B) Two

(C) Three

(D) Infinite

Question 8. The justification of the perpendicular bisector construction often uses the property of points equidistant from two points, which is typically proven using triangle ______.

(A) Similarity

(B) Congruence

(C) Area

(D) Perimeter

Question 9. The point where the perpendicular bisectors of the sides of a triangle intersect is called the ______.

(A) Incenter

(B) Centroid

(C) Orthocenter

(D) Circumcenter

Question 10. In constructing a perpendicular to a line from a point on the line, the initial step of drawing arcs of the same radius from the point intersecting the line creates a segment on the line with the point as its ______.

(A) Endpoint

(B) Midpoint

(C) Center of rotation

(D) Intersection

Question 1. To construct a line parallel to a given line through a point not on it, you can use the property that if a transversal intersects two lines such that corresponding angles are ______, then the lines are parallel.

(A) Supplementary

(B) Complementary

(C) Equal

(D) Bisected

Question 2. Another method to construct parallel lines uses the property that if alternate interior angles formed by a transversal are ______, the lines are parallel.

(A) Supplementary

(B) Complementary

(C) Equal

(D) Bisected

Question 3. The construction of parallel lines often involves the fundamental ability to ______ an angle accurately using compass and ruler.

(A) Measure

(B) Bisect

(C) Copy

(D) Estimate

Question 4. According to the Parallel Postulate, through a point not on a given line, there is exactly ______ line parallel to the given line.

(A) Zero

(B) One

(C) Two

(D) Infinite

Question 5. In the corresponding angles method, the copied angle is constructed at the external point in the ______ position relative to the transversal.

(A) Alternate interior

(B) Corresponding

(C) Vertically opposite

(D) Adjacent

Question 6. Two lines in the same plane that never intersect are called ______ lines.

(A) Perpendicular

(B) Intersecting

(C) Parallel

(D) Skew

Question 7. The justification for parallel line construction using angle properties relies on the ______ of the relevant angle theorems.

(A) Definitions

(B) Axioms

(C) Converses

(D) Corollaries

Question 8. A line that intersects two or more lines is called a ______.

(A) Parallel line

(B) Perpendicular line

(C) Transversal

(D) Chord

Question 9. Using set squares and a ruler is a practical method to draw parallel lines, but the standard compass and ruler method relies on ______ properties.

(A) Length

(B) Area

(C) Angle

(D) Volume

Question 10. If interior angles on the same side of a transversal are supplementary, then the two lines intersected by the transversal are ______.

(A) Perpendicular

(B) Intersecting

(C) Parallel

(D) Skew

Question 1. To divide a line segment AB in the ratio $m:n$ internally, you draw a ray AC from A and mark ______ equal parts on it.

(A) $m$

(B) $n$

(C) $m+n$

(D) $|m-n|$

Question 2. In the construction for dividing segment AB in ratio $m:n$ using ray AC, you first join the ______ point on AC to B.

(A) m-th

(B) n-th

(C) (m+n)-th

(D) 1st

Question 3. The construction for dividing a line segment in a given ratio is justified by the ______ Theorem.

(A) Pythagoras

(B) Angle Bisector

(C) Basic Proportionality

(D) Midpoint

Question 4. Dividing a line segment internally means finding a point that lies ______ the two endpoints.

(A) Outside

(B) Between

(C) On the extension of

(D) At the beginning of

Question 5. If a line segment is divided in the ratio $1:1$, the point of division is the ______.

(A) Endpoint

(B) Quarter point

(C) Midpoint

(D) Three-quarter point

Question 6. The Basic Proportionality Theorem states that if a line is drawn parallel to one side of a triangle intersecting the other two sides, it divides the two sides ______.

(A) Equally

(B) Proportionally

(C) Perpendicularly

(D) At right angles

Question 7. To mark equal parts on the ray AC, a ______ is used with a fixed opening.

(A) Ruler

(B) Protractor

(C) Compass

(D) Set square

Question 8. Dividing a line segment AB in the ratio $m:n$ requires the construction of ______ lines.

(A) Perpendicular

(B) Parallel

(C) Intersecting

(D) Skew

Question 9. If a line segment is divided in the ratio $1:2$, it is divided into ______ total equal parts on the auxiliary ray for construction purposes.

(A) 1

(B) 2

(C) 3

(D) 4

Question 10. The justification of line segment division construction relies on the concept of ______ triangles formed by the parallel line and the transversals.

(A) Congruent

(B) Equilateral

(C) Isosceles

(D) Similar

Question 1. To construct a triangle given the lengths of its three sides (SSS criterion), you draw one side as the base and then use the other two side lengths as ______ from the endpoints of the base.

(A) Angles

(B) Arcs

(C) Perpendiculars

(D) Parallel lines

Question 2. A triangle can be uniquely constructed if you are given two sides and the ______ angle.

(A) Opposite

(B) Adjacent

(C) Included

(D) Any

Question 3. When constructing a triangle using the ASA criterion, you are given two angles and the ______ side.

(A) Opposite

(B) Adjacent

(C) Included

(D) Longest

Question 4. To form a triangle with side lengths a, b, and c, the sum of the lengths of any two sides must be ______ than the length of the third side.

(A) Equal to

(B) Less than

(C) Greater than

(D) Half

Question 5. If you are given two angles and a non-included side (AAS criterion), you can find the third angle using the ______ property.

(A) Triangle Inequality

(B) Pythagorean

(C) Angle Sum

(D) Exterior Angle

Question 6. The minimum number of independent measurements required to uniquely construct a triangle (excluding cases like AAA) is ______.

(A) Two

(B) Three

(C) Four

(D) Five

Question 7. Which criterion is specifically for constructing right-angled triangles?

(A) SSS

(B) SAS

(C) ASA

(D) RHS

Question 8. If the sum of two angles given for ASA construction is $180^\circ$ or more, a triangle ______ be formed.

(A) Can

(B) Cannot

(C) May

(D) Will sometimes

Question 9. The construction of basic triangles relies heavily on the ______ criteria for establishing uniqueness.

(A) Similarity

(B) Congruence

(C) Area

(D) Perimeter

Question 1. To construct an equilateral triangle with side length 's', you can draw a base of length 's' and then draw arcs of radius 's' from ______ endpoints.

(A) One

(B) Both

(C) Any

(D) No

Question 2. All angles in an equilateral triangle are equal to ______ degrees.

(A) $30$

(B) $45$

(C) $60$

(D) $90$

Question 3. To construct an isosceles triangle given the base and equal sides, you use the ______ criterion.

(A) ASA

(B) SAS

(C) SSS

(D) RHS

Question 4. In an isosceles triangle, the angles opposite the equal sides (base angles) are ______.

(A) Complementary

(B) Supplementary

(C) Equal

(D) Obtuse

Question 5. The RHS criterion for constructing a right-angled triangle requires the hypotenuse and ______ to be given.

(A) Both legs

(B) One leg

(C) Both acute angles

(D) The perimeter

Question 6. The justification for constructing an equilateral triangle by drawing arcs of equal radius from the base endpoints relies on ensuring all ______ are equal.

(A) Angles

(B) Sides

(C) Altitudes

(D) Medians

Question 7. To construct an isosceles triangle given the base and base angles, you use the ______ criterion, drawing the angles at the endpoints of the base.

(A) SSS

(B) SAS

(C) ASA

(D) RHS

Question 8. In a right-angled triangle constructed using the RHS criterion, the angle between the two given sides (hypotenuse and leg) is ______.

(A) $30^\circ$

(B) $45^\circ$

(C) $90^\circ$

(D) Not necessarily a specific angle

Question 9. An isosceles triangle with a vertex angle of $60^\circ$ is also a/an ______ triangle.

(A) Right-angled

(B) Obtuse-angled

(C) Equilateral

(D) Scalene

Question 10. To construct an isosceles triangle given the base and vertex angle, you must first ______ the base angles using the angle sum property.

(A) Measure

(B) Estimate

(C) Calculate

(D) Bisect

Question 1. To construct a triangle given BC, $\angle B$, and AB+AC, you mark BD = AB+AC on the ray of $\angle B$ and construct the ______ of CD.

(A) Angle bisector

(B) Perpendicular bisector

(C) Median

(D) Altitude

Question 2. In the construction given BC, $\angle B$, and AB+AC, vertex A is found where the ray BD intersects the ______ of CD.

(A) Angle bisector

(B) Perpendicular bisector

(C) Median

(D) Altitude

Question 3. To construct a triangle given BC, $\angle B$, and $|AB-AC|$, you mark BD = $|AB-AC|$ on the ray of $\angle B$ (or its extension) and construct the ______ of CD.

(A) Angle bisector

(B) Perpendicular bisector

(C) Median

(D) Altitude

Question 4. To construct a triangle given two sides and a median, the standard method often involves forming a ______ by extending the median.

(A) Square

(B) Rhombus

(C) Rectangle

(D) Parallelogram

Question 5. In the construction given $\angle B, \angle C$, and perimeter, you draw a segment equal to the perimeter and construct angles equal to ______ at its ends.

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

(B) $(1/2)\angle B, (1/2)\angle C$

(C) $90^\circ - \angle B, 90^\circ - \angle C$

(D) $180^\circ - \angle B, 180^\circ - \angle C$

Question 6. In the perimeter construction, after finding vertex A, you construct the ______ of AP and AQ to find vertices B and C on the perimeter segment.

(A) Angle bisectors

(B) Medians

(C) Altitudes

(D) Perpendicular bisectors

Question 7. To construct a triangle given two angles and an altitude, you draw a line, mark the foot of the altitude, and construct a ______ line at that point where the vertex A will lie.

(A) Parallel

(B) Perpendicular

(C) Bisecting

(D) Secant

Question 8. The justification for constructions involving the sum or difference of sides often relies on the property that any point on the perpendicular bisector is ______ from the endpoints of the segment.

(A) Closer

(B) Further

(C) Equidistant

(D) Not related

Question 9. In the construction given two sides AB, AC and median AD, the intermediate triangle ACE (formed by extending AD) is constructed using the ______ criterion.

(A) ASA

(B) SAS

(C) SSS

(D) AAS

Question 1. To construct a triangle similar to $\triangle ABC$ with a scale factor $m/n$, you mark ______ equal parts on a ray BX from B.

(A) $m$

(B) $n$

(C) $m+n$

(D) $\text{max}(m, n)$

Question 2. If the scale factor is $m/n$ and $m < n$ (scaling down), you connect $B_n$ to C and draw a line through ______ parallel to $B_nC$.

(A) $B_m$

(B) $B_n$

(C) $B_1$

(D) $B_{m+n}$

Question 3. If the scale factor is $m/n$ and $m > n$ (scaling up), you connect $B_n$ to C and draw a line through ______ parallel to $B_nC$.

(A) $B_m$

(B) $B_n$

(C) $B_1$

(D) $B_{m+n}$

Question 4. The justification for similar triangle construction relies on the ______ Theorem.

(A) Pythagoras

(B) Angle Sum

(C) Basic Proportionality

(D) Midpoint

Question 5. If the scale factor is less than 1, the constructed similar triangle will be ______ than the original triangle.

(A) Larger

(B) Smaller

(C) Congruent

(D) Rotated

Question 6. After finding C' on BC (or its extension), you draw a line through C' parallel to ______ to find vertex A'.

(A) BC

(B) AB

(C) AC

(D) BX

Question 7. If a triangle $\triangle A'BC'$ is similar to $\triangle ABC$ with a scale factor $k$, the ratio of their areas is ______.

(A) $k$

(B) $k^2$

(C) $\sqrt{k}$

(D) $1/k$

Question 8. When scaling down ($m < n$), the constructed similar triangle is typically located ______ the original triangle, sharing a vertex.

(A) Outside

(B) Inside

(C) Adjacent to

(D) Overlapping

Question 9. The construction of similar triangles requires the ability to construct ______ lines.

(A) Perpendicular

(B) Parallel

(C) Bisecting

(D) Tangent

Question 10. If the scale factor is exactly 1, the constructed triangle is ______ to the original triangle.

(A) Smaller

(B) Larger

(C) Similar but not congruent

(D) Congruent

Question 1. To construct a general quadrilateral uniquely, you typically need ______ independent measurements.

(A) Three

(B) Four

(C) Five

(D) Six

Question 2. A unique quadrilateral can be constructed if you are given the lengths of its four sides and ______.

(A) One angle

(B) One diagonal

(C) Two angles

(D) The perimeter

Question 3. Which property is NOT always true for a parallelogram?

(A) Opposite sides are equal.

(B) Opposite angles are equal.

(C) Diagonals are equal.

(D) Diagonals bisect each other.

Question 4. When constructing a rectangle given its length and width, which construction ability is NOT required?

(A) Drawing a line segment of a given length.

(B) Constructing a $90^\circ$ angle.

(C) Constructing an angle bisector.

(D) Marking a point at a specific distance on a line.

Question 5. Which statement is NOT true about constructing a rhombus given the lengths of its two diagonals?

(A) The diagonals bisect each other at right angles.

(B) You draw one diagonal and construct its perpendicular bisector.

(C) You mark the full length of the second diagonal on the perpendicular bisector from the midpoint.

(D) The endpoints of the diagonals are the vertices of the rhombus.

Question 6. Which statement is NOT true about constructing a square given its side length 's'?

(A) You can use the property that all sides are 's' and all angles are $90^\circ$.

(B) You can construct a rhombus with side 's' and one angle $90^\circ$.

(C) You can construct a rectangle with length and width 's'.

(D) You only need to know the perimeter to construct a unique square.

Question 7. Which combination of measurements is NOT sufficient to uniquely construct a parallelogram?

(A) Two adjacent sides and the included angle.

(B) Two adjacent sides and a diagonal.

(C) Both diagonals and the angle between them.

(D) All four side lengths.

Question 8. Which statement is NOT true about dividing a quadrilateral into triangles for construction?

(A) A diagonal divides a quadrilateral into two triangles.

(B) If you can construct the triangles, you can construct the quadrilateral.

(C) The sum of the angles in a quadrilateral is equal to the sum of the angles in the two triangles it is divided into.

(D) The diagonal is always the shortest line segment connecting opposite vertices.

Question 9. Which property is NOT true for a square?

(A) All sides are equal.

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

(C) Diagonals are perpendicular.

(D) Diagonals are unequal.

Question 10. Which of the following quadrilaterals does NOT always have diagonals that bisect each other?

(A) Parallelogram

(B) Rectangle

(C) Rhombus

(D) Trapezium

Question 1. To construct a tangent to a circle at a point P on the circle (center O), you construct a line ______ to the radius OP at P.

(A) Parallel

(B) Perpendicular

(C) Intersecting

(D) Bisecting

Question 2. From a point outside a circle, ______ tangents can be drawn to the circle.

(A) One

(B) Two

(C) Infinite

(D) Zero

Question 3. To construct tangents from an external point P to a circle with center O, you construct a circle with ______ as diameter.

(A) OP

(B) Radius of original circle

(C) Distance from P to a point on the circle

(D) Any convenient segment

Question 4. The lengths of the two tangents drawn from an external point to a circle are ______.

(A) Unequal

(B) Equal

(C) Proportional to distance from center

(D) Related to the radius

Question 5. The justification for constructing tangents from an external point utilizes the property that the angle in a semicircle is ______ degrees.

(A) $60$

(B) $90$

(C) $120$

(D) $180$

Question 6. From a point inside a circle, ______ tangents can be drawn to the circle.

(A) One

(B) Two

(C) Infinite

(D) Zero

Question 7. The line segment from the center of a circle to the point of tangency is called the ______.

(A) Chord

(B) Diameter

(C) Radius

(D) Secant

Question 8. To construct a tangent at a point on the circle, you are essentially performing the construction of a ______ at that point.

(A) Angle bisector

(B) Perpendicular to a line from a point on it

(C) Parallel line

(D) Perpendicular bisector

Question 9. If two tangents from an external point meet at an angle $\theta$, the angle between the radii to the points of contact is ______.

(A) $\theta$

(B) $2\theta$

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

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

Question 10. The points where the auxiliary circle with diameter OP intersects the original circle are the ______ of the tangents from P.

(A) Centers

(B) Endpoints

(C) Points of tangency

(D) Vertices

Question 1. The role of justification in geometric constructions is to ______ that the constructed figure meets the required properties.

(A) Estimate

(B) Draw

(C) Prove

(D) Measure

Question 2. Justification in geometric constructions involves using basic geometric principles like axioms, postulates, and ______.

(A) Conjectures

(B) Opinions

(C) Measurements

(D) Theorems

Question 3. The justification for angle bisector construction relies on the property that any point on the bisector is ______ from the arms of the angle.

(A) Closer

(B) Further

(C) Equidistant

(D) Twice the distance

Question 4. The justification for the perpendicular bisector construction often uses ______ criteria to prove the equidistance property.

(A) Similarity

(B) Congruence

(C) Area

(D) Perimeter

Question 5. The justification for parallel line construction using angle properties relies on the ______ of the relevant angle theorems.

(A) Definitions

(B) Axioms

(C) Converses

(D) Postulates

Question 6. The justification for dividing a line segment in a given ratio is based on the ______ Theorem.

(A) Pythagoras

(B) Angle Sum

(C) Basic Proportionality

(D) Exterior Angle

Question 7. Verifying the accuracy of a construction using measurement tools provides ______ but not a formal geometric proof.

(A) Justification

(B) Proof

(C) Evidence

(D) Theorem

Question 8. A statement accepted as true without proof in geometry is called a/an ______ or postulate.

(A) Theorem

(B) Definition

(C) Axiom

(D) Conjecture

Question 9. Justification helps to understand ______ the construction method works.

(A) How

(B) Where

(C) When

(D) Why

Question 10. A logical sequence of steps used to prove a geometric statement is called a ______.

(A) Construction

(B) Conjecture

(C) Definition

(D) Proof