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# ABC is an isosceles triangle with AC = BC. If $AB^2 = 2AC^2$. Prove that ABC is a right triangle.

Given:

ABC is an isosceles triangle with AC = BC and $AB^2 = 2AC^2$.

To do:

We have to prove that ABC is a right triangle.

Solution:

In $∆ABC$,

$AB^2 = 2AC^2$.

$AB^2= AC^2 + AC^2$

$AB^2 = AC^2 + BC^2$

This implies, by converse of Pythagoras theorem,

$\angle ACB= 90^o$

Therefore,

ABC is a right triangle.

Hence proved.

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