Question

In an Isosceles ∆ PQR, ∠P = 90 Provethat:QR2 =2PQ2

Answer 1

To prove : PR² = 2PQ²

Given : PQR is an isosceles right triangle with ∠Q = 90°.

In the given triangle ,

∠Q = 90°

PR is the hypotenuse. And, QR = PQ as the triangle is isosceles.

By the Pythagoras theorem,

(Hypotenuse)² = (Opp. Side)² + (Adj.side)²

PR² = PQ² + QR²

PR² = PQ² + PQ²

PR² = 2PQ²

Therefore, It is proved that PR² = 2PQ²