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

Question

Philoid · Accepted Answer

Given an isosceles triangle ABC with AC = BC, and AB² = 2AC²

To Prove: ∆ABC is a right triangle

Proof: AB² = 2AC² (given)

⇒ AB² = AC² +AC²

⇒ AB² = AC² +BC² [∵AC =BC]

⇒ ∆ABC is a right triangle right angled at C.

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