Question

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.

PLEASE TELL ​

Answer 1

ANSWER

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.