Answer :


Given: Q is a right angle.


To prove: PS2 + QR2= PR2 + QS2


Proof:


It can be seen both the triangles ΔPQS and ΔPQR are right angled triangles.


Applying Pythagoras Theorem to ΔPQS gives,


PS2 = PQ2 + QS2 [ H2 = P2 + B2]


PQ2 = PS2 - QS2 ……………… (1)


Applying Pythagoras theorem to ΔPQR gives,


PR2 = PQ2 + QR2 [ H2 = P2 + B2]


Substituting PQ2 from (1) gives,


PR2 = (PS2 - QS2) + QR2


PR2 = PS2 - QS2 + QR2


PR2 + QS2 = PS2 + QR2


PS2 + QR2= PR2 + QS2


Hence proved.


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