I have two asymptotic triangles that are equivalent

Question

I am trying to prove that two triangles that are asymptotic are congruent. Given that they both have a side that is congruent and, but their angles are not congruent. SO, for example, $\triangle ABC$ has $\angle A = \angle B$, and in the other triangle, $\triangle DEF$, the angles $\angle E = \angle F$. I started out by contradiction so saying the two triangles are not equal. So, aside from the side that is congruent to the other triangle, the other sides are not. But I am stuck on what to do with the angles to.