Question

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

Answer 1

In given figure $ABCD$ is a quadrilateral.

$\Rightarrow$ In $△ABC$ and $△BAD$

$\Rightarrow$ $BC=AD$ [Given]

$\Rightarrow$ $\angle CBA=\angle DAB$ [Given]

$\Rightarrow$ $AB=BA$ [Common side]

$\therefore$ $△ABC\cong △BAD$ [By SAS criteria]

$\therefore$ $BD=AC$ [CPCT]