Question

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Explanation:

Step1: Identify the common side

In \(\triangle BAD\) and \(\triangle CDA\), \(\overline{AD}\cong\overline{DA}\) (Reflexive property of congruence: a segment is congruent to itself).

Step2: Apply SSS (Side - Side - Side) congruence criterion

We know that \(\overline{BD}\cong\overline{AC}\) (given), \(\overline{BA}\cong\overline{DC}\) (given), and \(\overline{AD}\cong\overline{DA}\) (from Step 1).
By the SSS (Side - Side - Side) congruence criterion, if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent. So, \(\triangle BAD\cong\triangle CDA\).

Answer:

\(\triangle BAD\cong\triangle CDA\) by the SSS (Side - Side - Side) congruence criterion.