Question

The diagonals of quadrilateral PQRS intersect at O, at right angles. Prove that PQ² + SR² = PS² + QR².

Answer 1

The diagonal of quadrilateral PQRS intersect at O, at right angles.

Applying Pythagoras theorem, in ∆PQR

PQ² + QR² = PR²   ...(i)

Applying Pythagoras theorem, in ∆PSR

PS² + SR² = PR²   ...(ii)

From (i) and (ii), we get

PQ² + QR² = PS² + SR² 

Hence, Proved.