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As ABC is a right angle triangle than we can say AB is the hypotenuse, AC is the base and similarly altitude be BC.

So, the Pythagorean theorem : (Hyp)^2 = (Base)^2 + (Altitude )^2

As the triangle is isosceles 2 sides will be same.
Thus, AC=BC

Putting this to (1) we get

so, AB^2=2AC^2(proved)

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