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Let us consider ABC as a right angled triangle with AB as hypotenuse,AC as height and BC as base.
It is given in the question that AC=BC and AB^2=2AC^2
Now ,in a right angled triangle ,
hypotenuse^2=base^2 +altitude^2
So according to the theorem in this case,
In the question it is clearly mentioned that AC=BC
Hence proved
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As ac = bc
so ac^2+bc^2 = ac^2+ac^2 = 2(ac)^2
acc to pythagorous thm
ab^2= ac^2 + bc^2 = 2(ac)^2 
so ab^2= 2ac^2
hence verified
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