Question

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

Answer 1

We are given

AC=BC(i), and

AB^2=2AC^2 (ii)

We can rewrite equation (ii) as

AB^2=AC^2 + AC^2

AB^2=AC^2 +BC^2  (iii)      (Given AC=BC so also AC^2=BC^2)

We know that the equation matches with the  Pythagoras  equation 

So triangle ABC is a isosceles right trianglewith AB as hypotenus and right angled at C that is 

angle ACB = 90⁰