In a quadrilateral ABCD angle A is equal to angle D is equal to 90 degree. Prove that AC square + BD square is equal to AD square + BC square + 2 CD multiply AB.
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A quadrilateral ABCD,
∠B =90°,
AD² = AB² + BC² + CD²
To Prove: ∠ACD = 90°
PROOF:
AD² = AB² + BC² + CD²
AD² - CD² = AB² + BC² ……………(1)
In right ∆ABC,
∠B =90°,
AC² = AB² + BC²……………….(2)
[By Pythagoras theorem]
From eq 1 & 2
AC² = AD² - CD²
AC² + CD² = AD²
Therefore , ∠ACD = 90°
[By converse of Pythagoras theorem]
Hence, proved.
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