Assertion (A): All the interior angles of a square are right angles.
Reason (R): Diagonals of a square intersect at right angles.
Assertion (A) is true, Reason (R) is false.
Assertion (A) is false, Reason (R) is true.
Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct reason for Assertion (A).
Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct reason (or explanation) for Assertion (A).
Answer
By definition, a square is a quadrilateral with four equal sides and four right angles (each 90°).
∴ Assertion (A) is true.
In a square, the diagonals bisect each other at 90°.
∴ Reason (R) is true.
∴ Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct reason (or explanation) for Assertion (A).
Hence, option 4 is the correct option.
Assertion (A): If one angle of a rhombus is 70°, then its largest angle is 110°.
Reason (R): Every rhombus is a square.
Assertion (A) is true, Reason (R) is false.
Assertion (A) is false, Reason (R) is true.
Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct reason for Assertion (A).
Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct reason (or explanation) for Assertion (A).
Answer
A rhombus is a quadrilateral where all four sides are equal in length.
In a rhombus opposite angles are equal.
If one angle of the rhombus is 70°, then its opposite angle is also 70°.
In a rhombus consecutive angles are supplementary (sum to 180°).
Consecutive angle = 180° − 70° = 110°.
The four angles of the rhombus would be 70°, 110°, 70° and 110°.
The largest angle among these is 110°.
∴ Assertion (A) is true.
A rhombus is a quadrilateral in which all four sides equal. Its angles are not necessarily 90°.
A square is a special type of rhombus where all four angles are also right angles (90°).
Therefore, while every square is a rhombus, not every rhombus is a square.
∴ Reason (R) is false.
∴ Assertion (A) is true, Reason (R) is false.
Hence, option 1 is the correct option.
Assertion (A): Diagonals of adjoining quadrilateral bisect each other. Then ∠B = 135°.
Reason (R): If diagonals of a quadrilateral bisect each other, then it is a parallelogram.
Assertion (A) is true, Reason (R) is false.
Assertion (A) is false, Reason (R) is true.
Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct reason for Assertion (A).
Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct reason (or explanation) for Assertion (A).
Answer
We know that,
In a parallelogram, diagonals bisect each other.
∴ Reason (R) is true.
Given,
Diagonals of quadrilateral ABCD bisect each other. Thus, ABCD is a parallelogram.
In a parallelogram, the sum of any two adjacent angles is always 180 degrees (supplementary).
⇒ ∠A + ∠B = 180°
⇒ 45° + ∠B = 180°
⇒ ∠B = 180° − 45° = 135°.
∴ Assertion (A) is true.
∴ Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct reason for Assertion (A).
Hence, option 3 is the correct option.