CBSE-Class-10-Maths-Assertion-and-Reason-Chapter-11-Constructions

Class 10^th Maths Chapter Assertion and Reason Questions

Question 1

Assertion (A): To construct a perpendicular bisector of a line segment, we need to use a compass and a straightedge.
Reason (R): The perpendicular bisector divides the line segment into two equal parts at a right angle.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: A) Both A and R are true, and R is the correct explanation of A.
Explanation: The construction of the perpendicular bisector requires a compass and straightedge, and it indeed divides the segment into equal parts at $90^\circ$ .

Question 2

Assertion (A): When constructing an angle of $60^\circ$ , we can use an equilateral triangle.
Reason (R): The angles of an equilateral triangle are all equal to $60^\circ$ .

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: A) Both A and R are true, and R is the correct explanation of A.
Explanation: Constructing an angle of $60^\circ$ can be achieved by using the properties of an equilateral triangle.

Question 3

Assertion (A): A compass can be used to draw arcs and circles.
Reason (R): A compass has two arms, one for the pencil and one for the point.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: A) Both A and R are true, and R is the correct explanation of A.
Explanation: The two arms of the compass facilitate drawing arcs and circles effectively.

Question 4

Assertion (A): It is necessary to measure the lengths of segments while constructing triangles.
Reason (R): Measurements ensure the triangle is constructed accurately according to the given dimensions.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: A) Both A and R are true, and R is the correct explanation of A.
Explanation: Accurate measurements are crucial for constructing triangles to ensure they meet the specified criteria.

Question 5

Assertion (A): When constructing a triangle given the lengths of all three sides, it is called a "SAS construction."
Reason (R): SAS stands for "Side-Angle-Side," which is applicable when one angle and two sides are given.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: D) A is false, but R is true.
Explanation: The assertion is incorrect; it should refer to "SSS construction," as SAS involves two sides and the included angle.

Question 6

Assertion (A): The angle of $90^\circ$ can be constructed using a right angle triangle.
Reason (R): A right angle triangle has one angle equal to $90^\circ$ .

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: A) Both A and R are true, and R is the correct explanation of A.
Explanation: A right angle triangle indeed has one angle equal to $90^\circ$ , which can be used to construct a right angle.

Question 7

Assertion (A): To construct a triangle with given base and height, one can draw a perpendicular from the vertex to the base.
Reason (R): The height of a triangle is the perpendicular distance from a vertex to the line containing the base.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: A) Both A and R are true, and R is the correct explanation of A.
Explanation: The height is indeed defined as the perpendicular distance from a vertex to the base.

Question 8

Assertion (A): A pair of compasses can be used to transfer distances accurately while constructing figures.
Reason (R): The compass maintains the same radius when transferring distances from one location to another.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: A) Both A and R are true, and R is the correct explanation of A.
Explanation: The compass does maintain the radius, allowing for accurate transfers of distance.

Question 9

Assertion (A): A square can be constructed using a straightedge and a compass.
Reason (R): A square consists of four equal sides and four right angles, which can be constructed using basic geometric tools.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: A) Both A and R are true, and R is the correct explanation of A.
Explanation: The construction of a square can indeed be achieved using a compass and straightedge, based on the properties of its sides and angles.

Question 10

Assertion (A): To bisect a given angle, the compass must be placed at the vertex of the angle.
Reason (R): The bisection of an angle requires equal arcs on both sides, which can only be achieved by placing the compass at the vertex.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: A) Both A and R are true, and R is the correct explanation of A.
Explanation: The compass needs to be placed at the vertex to ensure equal distances and angles are created.

Question 11

Assertion (A): The construction of a triangle with given two sides and included angle is known as SSS construction.
Reason (R): SSS stands for "Side-Side-Side," which is applicable when all three sides are given.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: D) A is false, but R is true.
Explanation: The assertion is incorrect; it should refer to "SAS construction," where two sides and the included angle are given.

Question 12

Assertion (A): The sum of angles in a triangle is always $180^\circ$ .
Reason (R): The angles in a triangle are formed by three intersecting lines.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: B) Both A and R are true, but R is not the correct explanation of A.
Explanation: The sum of angles in a triangle is always $180^\circ$ , but the reason is not correctly stating how these angles are formed.

Question 13

Assertion (A): The locus of points that are equidistant from a given point forms a circle.
Reason (R): A circle is defined as the set of all points that are at a fixed distance (radius) from the center.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: A) Both A and R are true, and R is the correct explanation of A.
Explanation: The definition of a circle aligns perfectly with the locus of points that are equidistant from a point.

Question 14

Assertion (A): The construction of a triangle requires only a ruler and a compass.
Reason (R): A ruler measures lengths, and a compass constructs circles and arcs.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: A) Both A and R are true, and R is the correct explanation of A.
Explanation: The tools required for constructing a triangle can be limited to a ruler and a compass.

Question 15

Assertion (A): To construct a tangent to a circle from a point outside the circle, you can use a right triangle.
Reason (R): The tangent to a circle is always perpendicular to the radius at the point of contact.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: A) Both A and R are true, and R is the correct explanation of A.
Explanation: The construction involves using properties of triangles and tangents.

Question 16

Assertion (A): A regular hexagon can be constructed using a compass and straightedge.
Reason (R): A regular hexagon can be inscribed in a circle.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: A) Both A and R are true, and R is the correct explanation of A.
Explanation: The construction of a regular hexagon involves inscribing it in a circle, which can be done with a compass and straightedge.

Question 17

Assertion (A): To construct a triangle with given two angles and the included side, it is called an "ASA construction."
Reason (R): ASA stands for "Angle-Side-Angle," applicable when two angles and the included side are given.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: A) Both A and R are true, and R is the correct explanation of A.
Explanation: The ASA construction principle states that a triangle can be constructed from two angles and the side between them.

Question 18

Assertion (A): The angle bisector of a triangle divides the triangle into two smaller triangles with equal areas.
Reason (R): The angle bisector theorem states that the angle bisector divides the opposite side into segments proportional to the other two sides.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: B) Both A and R are true, but R is not the correct explanation of A.
Explanation: While the angle bisector divides the triangle into two triangles of equal area, the reason given focuses on the ratio of segments rather than area equality.

Question 19

Assertion (A): A construction can be termed as "congruent" if two figures are of the same shape and size.
Reason (R): Congruence can be established by superimposing one figure over the other.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: A) Both A and R are true, and R is the correct explanation of A.
Explanation: Congruent figures have the same shape and size, and they can be shown to overlap perfectly when superimposed.

Question 20

Assertion (A): A chord that passes through the center of a circle is called a diameter.
Reason (R): A diameter is the longest chord in a circle.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: A) Both A and R are true, and R is the correct explanation of A.
Explanation: The definition of a diameter and its property as the longest chord are both accurate.

Question 21

Assertion (A): A point lies on the perpendicular bisector of a segment if it is equidistant from the endpoints of the segment.
Reason (R): The perpendicular bisector is defined as the locus of points that are equidistant from the segment's endpoints.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: A) Both A and R are true, and R is the correct explanation of A.
Explanation: The definition of the perpendicular bisector aligns with the property that any point on it is equidistant from the endpoints.

Question 22

Assertion (A): A triangle can be constructed if the lengths of two sides and the measure of the angle opposite one of the sides are known.
Reason (R): This is known as the "SSA construction."

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: C) A is true, but R is false.
Explanation: While the assertion is true, SSA is not a valid construction criterion because it may lead to ambiguous cases.

Question 23

Assertion (A): A cyclic quadrilateral is a quadrilateral whose vertices lie on a single circle.
Reason (R): The opposite angles of a cyclic quadrilateral are supplementary.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: A) Both A and R are true, and R is the correct explanation of A.
Explanation: The definition of a cyclic quadrilateral and the property of its angles both hold true.

Question 24

Assertion (A): To construct a triangle with given base and height, you must draw the height from the opposite vertex to the base.
Reason (R): The height creates two right triangles that can be used to find the third vertex.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: A) Both A and R are true, and R is the correct explanation of A.
Explanation: Drawing the height from the opposite vertex does indeed create right triangles, assisting in the construction of the triangle.

Question 25

Assertion (A): An equilateral triangle can be constructed with only a compass and straightedge.
Reason (R): An equilateral triangle has all sides of equal length.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: A) Both A and R are true, and R is the correct explanation of A.
Explanation: The construction of an equilateral triangle can be done using just a compass to ensure equal lengths.

Chapter 11 Constructions

Class 10th Maths Chapter Assertion and Reason Questions