Question

In an isosceles triangle ABC, if AC = BC and AB² = 2AC², then ∠C = ______.

Answer 1

In an isosceles triangle ABC, if AC = BC and AB² = 2AC², then ∠C = 90°.

Explanation:

Let AC = BC = a. Then AB² = 2a² = a² + a² = AC² + BC², so by the converse of the Pythagorean theorem the angle opposite AB (i.e., ∠C) is a right angle.