Question

PQR is isosceles right angle, right angled at Q. Prove that
${pr}^{2} = 2 {pq}^{2}$
​

Answer 1

Answer:

PR²=2PQ²

Step-by-step explanation:

Given:

• ∆PQR is isosceles,
• PQ=QR
• mQ=90°

To Prove:

• PR²=2PQ²

Proof:

• in ∆PQR , due to it is a right angled triangle,
• by Pythagorean theorem, PQ²+QR²=PR²........................................(i)
• due to it is a isosceles , PQ=QR......................................................(ii)
• now,by putting the value of QR from equation (ii) in equation (i), we get,
• PQ²+PQ²=PR²
• 2PQ²=PR²(proved)

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