Question

$ABC$ is an isosceles triangle and $\angle B={90}^o$, then show that ${AC}^2=2{AB}^2$.

Answer 1

$ABC$ is a right angle triangle.

Given that $A{C}^2=2A{B}^2$

$A{C}^2=A{B}^2+A{B}^2$ .....(Since it is isosceles $AB=BC$)

$A{C}^2=A{B}^2+B{C}^2$

The traingle is satisfying the pythagoras theorem.

Therefore, the given triangle is right-angle triangle.