Question

Assertion (A): If the diagonals of a quadrilateral bisect each other at right angles, then the quadrilateral is a rhombus.

Reason (R): A quadrilateral whose diagonals bisect each other at right angles must be a square.

Options

• A is true, R is false.

• A is false, R is true.

• Both A and R are true, and R is the correct reason for A.

• Both A and R are true, and R is the incorrect reason for A.

Answer 1

A is true, R is false.

Explanation:

• Assertion (A): If the diagonals of a quadrilateral bisect each other at right angles, it satisfies the required properties of a parallelogram with perpendicular diagonals, making it a rhombus. Thus, Assertion (A) is true.
• Reason (R): For a quadrilateral to be a square, its diagonals must be both equal in length and bisect each other at right angles. A rhombus has perpendicular bisecting diagonals, but its diagonals are not necessarily equal in length; therefore, it does not have to be a square. Thus, Reason (R) is false.