Final answer:
The proof that triangles ABC and CDA are congruent is not complete without additional information. Based on the given data of angle and side congruence, the SAS postulate for congruency may be applicable, but more details are needed to finalize the proof.
Step-by-step explanation:
To prove that triangles ABC and CDA are congruent, we utilize the given information that angle BC is congruent to angle AD and AB is congruent to CD. This information suggests the possibility of applying the Side-Angle-Side (SAS) postulate for congruency of triangles which states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the triangles are congruent.
First, we establish that AB is congruent to CD by the given. Next, we recognize that angle BC is congruent to angle AD. To apply SAS, we also need to show that the sides including those angles are congruent. However, the question doesn't explicitly provide this information. Therefore, the provided question lacks sufficient detail to complete the proof based on the given information. If additional details or missing information were provided, such as the congruity of the third pair of sides (BC and DA), only then could we successfully apply the SAS postulate and conclude that triangle ABC is congruent to triangle CDA.