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