SSS congruence
SSS is the simplest of the congruence criteria: if the three sides of one triangle are equal to the three sides of another, the two triangles are congruent. Once the three side lengths are fixed, the triangle has no freedom left — the angles are forced. A triangle is rigid; that is why triangular bracing holds a bridge or a bookshelf steady, while a four-sided frame can still rack and lean.
Precisely: if in triangles ABC and DEF you have |AB| = |DE|, |BC| = |EF|, and |CA| = |FD|, then triangle ABC is congruent to triangle DEF, and consequently all three pairs of angles are equal too. The intuition: try to build a triangle from three given stick lengths. There is essentially one way to close it up (the mirror image counts as the same triangle), so three sides determine the shape completely. This is why SSS works and why three sticks of fixed length cannot wobble.
Two honest caveats. First, the three lengths must actually be able to form a triangle at all — they must satisfy the triangle inequality, with each side shorter than the sum of the other two. Second, SSS is a real criterion, unlike the false 'SSA'; having two sides and a non-included angle equal is not enough to force congruence.
Triangle ABC has sides 7, 9, 12; triangle PQR has sides 7, 9, 12 matched in order. By SSS the triangles are congruent, so (for instance) the angle opposite the side of length 12 is equal in both.
Three matching sides lock the triangle's shape completely.
Three given lengths must obey the triangle inequality, or no triangle exists at all. SSS is valid; the superficially similar 'SSA' (two sides and a non-included angle) is not a congruence criterion.