Question

PQRS is a rectangle. Prove that PR² + QS² = PQ² + QR² + RS² + PS².

Answer 1

Pythagoras theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Given,

In △PQR,

⇒ PR² = PQ² + QR²

In △SRQ,

⇒ SQ² = SR² + RQ²

Add the above equations,

⇒ PR² + QS² = PQ² + QR² + RS² + PS²

Hence proved.