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  1. An answer:

    I am not sure it was right, but here goes:

    It centers on showing triangles DAB and CBA are congruent.

    Proof:

    AD=BC (given), angle DAB=CBA (given),
    If segment AB=AB (reflexive property) (AB is a side of both triangles) then by
    Side-angle-side the triangles DAB and CBA are congruent. If that is the case then angles,CAB=DBA which proves triangle ABE is isosceles.

    I think you can also drop a bisector through E and prove it as well.

    JMM

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