Given that triangle ABE is isosceles with base BE and that BD≈EC justify why triangle ABD≈ AEC

Side-Angle-Side similarity is what will tell you that ABD ≈AEC.

Step-by-step explanation:

Since ABE is isosceles, that means that AB=AE, and that angles B and E are equal. In the problem they tell you that BD is congruent to EC, so you have the three pieces of information that you need. The angle is between the two sides, so triangles ABD and AEC are congruent by Side-Angle-Side similarity.