Question

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Explanation:

Step1: Analyze the given congruent parts

We are given $\overline{AD}\cong\overline{CD}$, $\overline{AB}\cong\overline{CB}$, and $\angle A\cong\angle C$.

Step2: Recall the SAS (Side - Angle - Side) congruence criterion

The SAS congruence criterion states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.
In $\triangle ABD$ and $\triangle CBD$, $\overline{AD}\cong\overline{CD}$, $\angle A\cong\angle C$, and $\overline{AB}\cong\overline{CB}$. Here, the angle ($\angle A$ and $\angle C$) is between the two sides ($\overline{AD}$ and $\overline{AB}$ in $\triangle ABD$; $\overline{CD}$ and $\overline{CB}$ in $\triangle CBD$)

Answer:

SAS