Question
In Figure, AX bisects $\angle\text{BAC}$ as well as ∠BDC. State the three facts needed to ensure that $\triangle\text{ACD}\cong\triangle\text{ABD}$.
✓
Answer
As per the given conditions, $\angle\text{CAD}=\angle\text{BAD}$ and $\angle\text{CDA}=\angle\text{BDA}$ (because AX bisects $\angle\text{BAC}$)
AD = DA (common)
Therefore, by ASA, $\triangle\text{ACD}\cong\triangle\text{ABD}$.
AD = DA (common)
Therefore, by ASA, $\triangle\text{ACD}\cong\triangle\text{ABD}$.
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