How to prove if a triangle is isosceles.

Question

If you have an isosceles triangle DAE inside another triangle CAB and CD is congruent to EB how do you prove that triangle CAB is isosceles?

Answer 1

Presumably it is given that CAB is isosceles. You can prove that triangle CDA is congruent to triangle BEA. (How? Remember, the main thing with isosceles triangles is that the base angles are congruent to each other.) From there you can use CPCTC to show DAE is isosceles.