Since AD and BE are perpendicular bisectors of each other, we can conclude:
[tex]\begin{gathered} CA=CD \\ CE=CB \end{gathered}[/tex]Besides, ∠ACB and ∠ECD are vertical angles, so, we can conclude:
[tex]\angle ACB=\angle ECD[/tex]If two sides and the included angle of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent, therefore:
[tex]\Delta ACB\cong\Delta DCE[/tex]By Side-Angle-Side (SAS) Congruence.