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Question
In a quadrilateral ABCD, ∠B = 90°. If AD2 = AB2 + BC2 + CD2 then prove that ∠ACD = 90°.
Solution
In quadrilateral ABCD, we have
∠B = 90°
So, `AC^2=AB^2+BC^2` (Pythagoras theorem)
and
`AD^2=AB^2+BC^2+CD^2` (Given)
So,
`AD^2=AB62+BC^2+CD^2`
`AD^2=AC^2+CD^2`
Hence, ∠ACD = 90° (Converse of Pythagoras theorem)
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