Question

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

Answer 1

In an isosceles ∆ABC,

AB² = 2AC² (Given)

⇒ AB² = AC² + AC²

⇒ AB² = AC² + BC² (AC = BC)

Using converse of Pythagoras theorem, we have

∆ABC is an isosceles right triangle right angled at C.

(In a triangle, if the square of one side is equal to the sum of the squares of other two sides, then the angle opposite to side is a right angle.)

∴ ∠C = 90º

In an isosceles triangle ABC, if AC = BC and AB² = 2AC², then ∠C = ___90º___.