In the figure 2.22, M is themidpoint of QR. ∠PRQ = 90°. Prove that, PQ2 = 4PM2 – 3PR2

In ∆PRQ, PRQ = 900

PQ2 = PR2 + QR2 – – – 1

In ∆PRM, PRM = 900

PM2 = PR2 + MR2

PM2 = PR2 + 2 [ M is midpoint]

4(PM2 – PR2) = QR2 – – – 2

1 And 2 implies

PQ2 = PR2 + 4(PM2 – PR2)

PQ2 = 4PM2 – 3PR2

PROVED.

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