Q11 of 53 Page 153

In ΔPQR, m∠Q = 90, M and N . Prove that PM2 + RN2 = PR2 + MN2.

11.JPG


mQ = 90


Applying Pythagoras theorem


PM2 = QM2 + PQ2


RN2 = QN2 + QR2


Adding the above two equations we get


PM2 + RN2 = QM2 + PQ2 + QN2 + QR2


⇒ PM2 + RN2 = (QM2 + QN2) + (PQ2 + QR2)


⇒ PM2 + RN2 = MN2 + PR2


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