Question

$ABCD$ is a quadrilateral in which $AD=BC$ and $\angle DAB=\angle CBA$ prove that
$\angle ABD=\angle BAC$

Answer 1

To Prove : $\Delta ABD\cong$ $\Delta BAC$

Proof: In quadrilateral $ABCD$, $AD=BC$ and $\angle DAB=\angle CBA$

In $\Delta ABD$ and $\Delta BAC$, we have

$AD=BC$ Given

$\angle DAB=\angle CBA$ (given)

$AB=AB$ (common)

$\Delta ABD\cong \Delta BAC$. [ by SAS congurency]

Since $\Delta ABD\cong \Delta BAC$,

$\angle ABD=\angle BAC$ [CPCT]