Final answer:
Triangles BAC and DCA are congruent by the ASA (Angle-Side-Angle) congruence criterion due to the congruence of two pairs of angles and the common side AC between them.
Step-by-step explanation:
If ∠BCA ≅ ∠DAC and ∠BAC ≅ ∠DCA, then ΔBAC ≅ ΔDCA by ASA (Angle-Side-Angle) congruence criterion. This criterion states that two triangles are congruent if two angles and the side between them in one triangle are equal to the corresponding two angles and side in the other triangle. In this case, we have two pairs of angles (∠BCA and ∠DAC, ∠BAC and ∠DCA) that are given as congruent. The side between these angles in both triangles (∠BCA and ∠BAC) is the common side AC, thus satisfying the ASA criterion.