SAS congruence
SAS says: if two sides of one triangle and the angle squeezed between them are equal to two sides and the included angle of another, the triangles are congruent. The crucial word is 'included' — the angle must be the one nestled between the two named sides, like the hinge between the two arms of a folding ruler. Fix the two arm-lengths and the hinge angle, and the far ends are pinned in place.
Precisely: if in triangles ABC and DEF you have |AB| = |DE|, angle A = angle D (the angle at the common vertex of those two sides), and |AC| = |DF|, then triangle ABC is congruent to triangle DEF. The reasoning is the folding-ruler picture: two sides leave the vertex at a fixed angle, so the third vertex of each is determined, and the third side and remaining two angles must match. From there CPCTC gives every other equality.
The single most important caution is the position of the angle: it must be between the two sides. If instead the equal angle lies outside, opposite one of the sides, you have 'SSA', which is not a valid criterion — it can leave two genuinely different triangles (the ambiguous case). So always check that the angle is the included one before invoking SAS.
In triangles ABC and DEF, |AB| = |DE| = 5, angle A = angle D = 40 degrees, and |AC| = |DF| = 8. Since the equal angle is included between the two equal sides, SAS gives triangle ABC congruent to triangle DEF.
Two sides and the angle between them pin the triangle down.
The angle must be included (between the two sides). The same data with the angle opposite a side is 'SSA', which does not force congruence — it can yield two different triangles.