AD=BE Given
AD + DE = BE + DE Equals plus Equals are equal
AE = BD Collinear property (from given line ADEB)
CD = CE Given
CDE is isosceles Def
angle CDE = angle CED prop isosceles triangles
AEC = BDC That's congruency, SAS (AE=BD, CE=CD, and the included angle)
AC = BC congruent parts of congruent triangles