# Prove that In a right-angled traingle, the square on the hypotenuse is equal to the sum of squares on the other two sides

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by karankeshari

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by karankeshari

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In a right angled triangle ABC, angle B=90°

construction:- draw BD perpendicular to AC

proof:-

∆ABC~∆BDC

by B.P.T

BC/AC=DC/BC

BC²=AC×DC -- eq1

also, ∆ABC~∆ADB

by B.P.T

AB/AC=AD/AB

AB²=AC×AD-- eq2

so, add eq 1 and 2 AB²+BC²=(AC×DC)+ (AC×AD)

AB²+BC²=AC(DC+AD)

AB²+BC²=AC×AC

W.K.T, AC=AD+DC

SO, AB²+BC²=AC²

Hence proved

B.P.T= basic proportionality theorem

W.K.T= we know that

~ = is similar to