Question

ABC is an isosceles triangle with AC = BC. If AB² = 2AC², prove that ABC is a right triangle.

Answer 1

Given that

AB² = 2AC²

⇒ AB² = AC² + AC²

⇒ AB² = AC² + BC² (As AC = BC)

The triangle is satisfying the pythagoras theorem

Therefore the given triangle is a right angle trangle