Question

$ABCD$ is a square, $X$ and $Y$ are points on sides $AD$ and $BC$ respectively, such that $AY=BX$. Prove that.
$\angle BAY=\angle ABY$

Answer 1

Given:$AY=BX$

$ABCD$ is a square

To prove that:$\angle BAY=\angle ABX$

Proof:

In $△ABY$ and $△ABX$

$AB=AB$ (common)

$AY=BX$ (given)

$\angle XAB=\angle YBA$ (${90}^{\circ }$ each)

$\therefore △ABY\cong △ABX$

$\therefore$ By $C.P.C.T\angle BAY=\angle ABX$