Question

ΔABC is isosceles with AC = BC. If AB² = 2AC², then find the measure of ∠C.

Answer 1

Given, AB² = 2AC²

⇒ AB² = AC² + AC²

⇒ AB² = BC² + AC²   ...(∵ Given, BC = AC)

It satisfies the pythagoras theorem.

So, according to converse of Pythagoras theorem, ΔABC is a right angle triangle and ∠C = 90°.