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

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#### Solution

Given that

AB^{2} = 2AC^{2}

⇒ AB^{2} = AC^{2} + AC^{2}

⇒ AB^{2} = AC^{2} + BC^{2} (As AC = BC)

The triangle is satisfying the pythagoras theorem

Therefore the given triangle is a right angle trangle

Concept: Right-angled Triangles and Pythagoras Property

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