The prove, angle CAE is congruent to angle CEA. is achieved using AAS congruence theorem and Isosceles triangle theorem
How to complete the proof
The two column proof is written as follows
Statement Reason
∠ BAC ≅ ∠ DEC given
∠ ABC ≅ ∠ EDC given
BC ≅ DC given
Δ ABC ≅ Δ ΕDC AAS congruence theorem
Δ ACE Definition of isosceles
∠ CAE ≅ ∠ CEA Base angles of Isosceles triangle are congruent