ΔABC is an isosceles triangle with AC = BC. If AB 2 = 2AC 2 , prove that ΔABC is a right triangle.

Question

Philoid · Accepted Answer

Given:

AC = BC

AB² = 2AC² …(Equation 1)

Equation 1 can be rewritten as

AB² = AC² + AC²

Since AC = BC we can write

AB² = AC² + BC² …Equation 2

Equation 2 represents the Pythagoras theorem which states that

Hypotenuse² = Base² + Perpendicular²

Since Pythagoras theorem is valid only for right-angled triangle so

So ABC is a right angled triangle right angled at C

Hence Proved