The statement that should be placed at the end of the proof is:
Finally, corresponding parts of congruent triangles are congruent by the CPCTC Theorem, so ∠A≅∠C.
This follows logically from the earlier steps of the proof, which establish that triangles ABD and CBD are congruent. Since corresponding angles of congruent triangles are also congruent, we conclude that the angles at A and C are congruent as well.