The reason the triangles are congruent by AAS is the following:
*Angles that oppose congruent sides are congruent and vice-versa, from this, we will have that the triangles have at least two congruent sides and two congruent angles, and by theorem the last angle will also be congruent (And as stated before) the side opposite to the last angle is congruent with the corresponding angle in the other triangle.