Answer:
1. BD bisects <CBE, AE || BD (Given)
2. <EBD ~= <CBD (Definition of < Bisectors)
3. <AEB ~= <EBD (Alternate Interior Angles Theorem)
4. <CAE ~= <CBD (Corresponding Angles Postulate)
5. <CAE ~= <AEB (Transitive Property of Congruence)
6. AB ~= BE (Converse of Isosceles Triangles Theorem)