Question

ΔАВС is a isosceles triangle in which AB = AC and ∠A = 90°. Prove that : BC² = 2AC².

Answer 1

Given:

ΔABC with AB = AC isosceles and ∠A = 90°.

To Prove:

BC² = 2AC².

Proof (Step-wise)]:

1. Because ∠A = 90°, sides AB and AC are the two legs and BC is the hypotenuse of right triangle ΔABC.

2. By the Pythagorean theorem for right triangle ΔABC.

BC² = AB² + AC²

3. Given AB = AC.

So, AB² = AC².

Substitute into step 2:

BC² = AC² + AC²

= 2 × AC²

Therefore, BC² = 2AC², as required.