In a quadrilateral ABCD, ∠ B = 90°, AD² = AB² + BC² + CD². Prove that ∠ACD = 90°.

Given: B = 90˚ in quadrilateral ABCD

AD2 = AB2 + BC2 + CD2

To prove: ACD = 90˚

Proof:

In ABC,

AC2 = AB2 + BC2 ….(i) [Pythagoras theorem]

Given AD2 = AB2 + BC2 + CD2

AD2 = AC2 + CD2 [from (i)]

In triangle ACD, ACD = 90˚ [Converse of Pythagoras theorem]

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