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

 Given :-
           ( i ) AB = AC
            ( ii ) BC² = 2AB²
To prove :-
          ABC is a right-angled triangle
Proof :-
        Given that
                          BC²= 2AB²
                          BC² = AB² + AB²
         But, AB = AC.
          So, AB²= AC².
So,
                          BC² = AB² + AC²
This triangle is satisfying Pythagoras Theorem. So, the given triangle is a right-angled triangle.


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