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By pythagoras theorem of a²+b²=c² we can prove it. As A =B, we can safely arrive at conclusion that Sides opposite to these two Angles are equal So 2AC²=AB² means that this is right angle triangle

A=B which means BC=AC AB^2=2AC^2......(given) AB^2=AC^2+AC^2 AB^2=AC^2+BC^2 but this is Pythagoras theorem therefore ∆ABC is right angled triangle with AB as hypotenuse