Question

PQR is a isosceles right triangle right Angled at Q prove the PR 2 =2 PQ2​

Answer 1

ANSWER:

As ΔPQR is right angled at R, then,

PQ

2

=QR

2

+PR

2

Since the triangle is an isosceles triangle, then, QR=PR, therefore,

PQ

2

=PR

2

+PR

2

PQ

2

=2PR

2

Hence proved.

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Answer 2

Answer: In isosceles triangle two sides are equal.

Given = pq ≈ qr

To prove = pr^2≈2pq^2

Proof = Acc. to pythagoras theorem,

pr^2 = pq^2 + qr^2

pr^2 = pq^2 + pq^2 { pq≈qr}

pr^2 = 2pq^2

Hence proved.