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Question
In a quadrilateral ABCD, ∠B = 90°, AD2 = AB2 + BC2 + CD2, prove that ∠ACD = 90°.
Solution
We have, ∠B = 90° and AD2 = AB2 + BC2 + CD2
∴ AD2 = AB2 + BC2 + CD2 [Given]
But AB2 + BC2 = AC2 [By pythagoras theorem]
Then, AD2 = AC2 + CD2
By converse of by pythagoras theorem
∠ACD = 90°
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