Definition: The AAS criterion states that if two angles and a non-included side of one triangle match those of another, the triangles are congruent.
How does AAS differ from ASA?
In ASA the side lies between the two angles. In AAS it is next to only one of them. Since the angles in a triangle sum to 180 degrees, knowing two angles gives the third, so AAS can always be converted into ASA.
When is it used?
When a figure gives two angle pairs and a side that touches only one of those angles, as with a shared side opposite a known angle.
Example. In triangle ABC, angle A = 52 degrees, angle B = 61 degrees, and BC = 14, the side opposite A. In triangle DEF, angle D = 52 degrees, angle E = 61 degrees, and EF = 14, the side opposite D. The third angles are both 67 degrees, so the included sides AB and DE would also be equal in a unique triangle. The triangles are congruent by AAS.
What should you avoid?
Using AAA or SSA, which are not criteria for congruence. The sides must correspond: the equal sides must both be opposite equal angles, or both adjacent in the same way. Check your labels before concluding.