Question

$ABCD$ is a square, $X$ and $Y$ are points on sides $AD$ and $BC$ respectively, such that $AY=BX$. Prove that.
$BY=AX$

Answer 1

In $\Delta ABY$ and $\Delta BAX$

$\angle A=\angle B$ (Right angles)

$BX=AY$ (Given)

$AB=AB$ (Common)

So, $\Delta ABY\cong \Delta BAX$ (RHS outeria)

so, $BY=AX$ (Using CPCT)

and $BX=AY$ (Using CPCT)