In order to prove that triangle ABE is congruent to triangle CBD by ASA we would need to show that

Two congruent triangles have the same shape as well as the
same size.

There are many ways to determine the congruence
of two triangles. Three fundamental conditions of congruence are SSS, SAS and
ASA.

Using ASA, two triangles are congruent if two of their
angles have the same measure and the included side has the same length in both the
triangles.

For the triangles you have provided: ABE and
CBD, let the measures of the angles be A, B, E, C and D and let the lengths of the sides
be ab, be, ea, cb, bd, and dc.

The triangles can be shown
to be congruent in many ways two of which are:

• A
  = C and ab = cb

• E = D and be = bd