AAS congruence
AAS says: if two angles of one triangle and a side not between them (a side opposite one of the angles) are equal to the corresponding two angles and side of another, the triangles are congruent. It is the same idea as ASA, only the known side sits beside the angle pair rather than between them.
Precisely: if in triangles ABC and DEF you have angle A = angle D, angle B = angle E, and a non-included side equal, say |BC| = |EF| (where BC is opposite angle A, not between angles A and B), then triangle ABC is congruent to triangle DEF. The reason AAS is automatically valid is the angle-sum theorem: knowing two angles pins down the third, m(angle C) = 180 - m(angle A) - m(angle B), so you really know all three angles and one side, which is exactly the ASA data once the third angle is filled in. AAS is therefore not an extra magic rule but ASA in disguise.
Take care that the matched side truly corresponds — that it is opposite equal angles in both triangles. And do not slide into 'SSA' (two sides and a non-included angle), which looks superficially similar but swaps a known angle for a known side and is not a valid criterion; the ambiguous case lurks there.
In triangles ABC and DEF, angle A = angle D = 50, angle B = angle E = 60, and side |BC| = |EF| = 9, where BC is opposite angle A. By AAS the triangles are congruent (the third angles are both 70).
Two angles and a non-included side also fix the triangle.
AAS works only because the angle sum determines the third angle, reducing it to ASA. Do not confuse it with 'SSA' (two sides, non-included angle), which is not valid.