Question

In triangle ABC, angle A=angle B. If AB square=2AC square, prove that ABC is right angled triangle.

Answer 1

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

Answer 2

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