Question

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

Answer 1

In order to prove angle it is enough to prove that .

Given,

.....(1)

Since, so applying Pythagoras theorem in the right angled triangle ABC, we get

.....(2)

From (1) and (2), we get

Therefore, angle . (Converse of pythagoras theorem)