AC and CD are congruent, because C is the midpoint of AD. , this also means
BC and CE are congruent, because C is the midpoint of BE.
Angles ACB and DCE are vertical angles which mean they are also congruent.
Using the Side-Angle- Side theorem, Triangles ABC and DEC are congruent.
This means AB and DE are congruent, because corresponding sides of congruent triangles are congruent.
