Answer:
1) AE = EC
2) AC is the perpendicular bisector of BD
3) ED = ED
3) AD = DC
4) ∆BAD = ∆BCD
5) <BAD = <BCD
Explanation:
1) By definition with a midpoint, the line that is divided creates two congruent segments.
2) Since AE and EC are congruent, the same side interior angle postulate shows that AEB and CEB are right angles thus making AC the perpendicular bisector of BD.
3) By definition of the reflective property, ED is equal to ED.
4) according to SSS congruence, the triangles are congruent.
5) according to CPCTC (corresponding parts of congruent triangles are congruent), the corresponding angles are congruent.
Hopefully I didn't include an unnecessary step, hope this helps!