If we're assuming ABC IS a triangle then:
First we need to prove that the two smaller triangles are congruent. We can see from the given facts that they each have 2 equivilent angles. Since all angles in any triangle must add up to give 180, the other angle of each triangle must also be equal. Now, this proves that the triangles are SIMILAR but it doesnt prove that they are congruent. To do that we need to prove one more thing. All you need to do is say that side BD is a shared side and is therefore equal. This proves that the triangles are congruent via Angle,side,angle equivilency proof. The next step is you say BA = BC because corresponding side lengths in congruent triangles are equivilent.
Sorry i see that was two days ago... most likely no longer relavent but it might help you or some one else lol... if you have any more question please post them ill do my best to answer them