Question

In figure $AX$ bisects $\angle BAC$ as well as $\angle BDC$. State the three facts needed to ensure that $\Delta ACD\cong \Delta ABD$.

Answer 1

As per the given conditions,

$\angle CAD=\angle BADand\angle CDA=\angle BDA$ (because $AX$ bisects $\angle BAC$)

AD = DA (common)

Therefore, $\Delta ACD\cong \Delta ABD$ (By ASA congruence rule)