# I have drawn a tr 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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