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Construction of an Angular Bisector and its Proof

In figure, AX...

Question

In figure, AX bisects $∠$ BAC as well as $∠$ BDC. State the three facts needed to ensure that $△$ ACD $≅$ $△$ ABD

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Solution

As per the given conditions.
$∠$ CAD = $∠$ BAD and $∠$ CDA = $∠$ BDA (because AX bisects $∠$ BAC)
AD = DA (common)
Therefore, by ASA, $△$ ACD $≅$ $△$ ABD

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