Question

Assertion: The diagonals of a square PQRS intersect at O. Then ΔPOQ is an isosceles right-angled triangle.

Reason: The diagonals of a square are equal and bisect each other at 90°.

Options

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

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

• A is true but R is false.

• A is false but R is true.

Answer 1

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

Explanation:

• A square has all sides equal and all angles 90°.
• The diagonals of a square are equal in length.
• These diagonals bisect each other at right angles (90°).
• Point O is the intersection of diagonals, thus it is the midpoint for both diagonals.
• Triangle POQ is formed by half of both diagonals, i.e. segments PO and QO.
• Since diagonals are equal and bisect each other, PO = OQ (both are half of the same diagonal).
• The angle at O between PO and QO is 90° because the diagonals intersect perpendicular to each other.
• Therefore, ΔPOQ has two equal sides and an included angle of 90°, which makes it an isosceles right-angled triangle.