Question

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

Answer 1

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=AB^2+BC^2+CD^2`

`AD^2=AC^2+CD^2`

Hence, ∠ACD = 90°                   (Converse of Pythagoras theorem)