ASA Theorem?

Suppose 2 triangles have 2 pairs of congruent angles. Suppose we also know that the side between each set of given angles (in one triangle) is congruent to the side between this same pair of angles in the other triangle. Does knowing only this constitute sufficient evidence to prove the triangles congruent? If so, explain how/why with respect to the transformations and/or triangle congruence theorems you've previously learned. If not, clearly explain why not.

Quick (Silent) Demo