Question

PQR is an isosceles right triangle with ∠Q = 90°. Prove that PR² = 2PQ²

Answer 1

Solution :

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

Answer 2

Given : isosceles ∆PQR

<Q = 90° ,

PQ = QR ---( 1 )

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By Phythogarian theorem:

In a triangle , the square of length of

the hypotenuse is equal to the sum

of the squares of lengths of the other

two sides .

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In ∆PQR ,

PR² = PQ² + QR²

=> PR² = PQ² + PQ² [ from ( 1 ) ]

=> PR² = 2PQ²

Hence, proved.

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