Question

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

Answer 1

We have, ∠B = 90° and AD² = AB² + BC² + CD²

∴ AD² = AB² + BC² + CD²   ...[Given]

But AB² + BC² = AC²   ...[By pythagoras theorem]

Then, AD² = AC² + CD²

By converse of pythagoras theorem

∠ACD = 90°