In the given figure:
[tex]\begin{gathered} AE=BE \\ \angle1\cong\angle2 \end{gathered}[/tex]
Angles 3 and 4 are vertical angles, therefore, they are congruent.
Thus, triangles ACE and BDE are congruent by AA Congruence Theorem.
Since one pair of sides (AE and BE) is equal, it means all the other corresponding sides are also equal
Therefore:
[tex]CE\cong DE[/tex]
