Question

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

Answer 1

$ABCD$ is a quadrilateral, where $AD=BC$ and $\angle DAB=\angle CBA$

In $△ABD$ and $△BAC,$

$\Rightarrow AD=BC$ [ Given ]

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

$\Rightarrow AB=BA$ [ Common side ]

$\therefore$ $△ABD\cong △BAC$ [ SAS Congruence rule ]
By CPCT,

$\therefore$ $\angle ABD=\angle BAC$