Question

In the given figure, if ABCD is a quadrilateral in which AD = BC and $\angle DAB=\angle CBA$, then

• A. $\Delta ABD\cong \Delta BAC$
• B. $BD=AC$
• C. $\angle ABD=\angle BAC$
• D. All of these

Answer 1

The correct option is D All of these

In $\Delta ABD$ and $\Delta BAC$
$AD=BC$(given)
$\angle DAB=\angle CBA$(given)
$AB=AB$ (common)
$\therefore \Delta DAB\cong \Delta CBA$ (by SAS congruence criterion )
$\Rightarrow \Delta ABD\cong \Delta BAC$
$AD=BC$ (CPCT)
$\angle ABD=\angle BAC$ (CPCT)
Thus all of this are correct.
So, the correct answer is (d).