Congruence

When is one triangle a copy of another? Congruence as a rigid motion that carries one figure exactly onto the other — and the criteria that pin a triangle down.

Congruent Triangles & Rigid Motion
Congruent
SSS & SAS
You rarely get to slide one triangle onto another — you get a handful of measurements. Which measurements are enough to force congruence? Discover the first two shortcuts by trying, and failing, to build a different triangle.
ASA & AAS
Two of the three parts that lock a triangle can be angles. Give a triangle a side and two angles and the rays meet at exactly one point — discover the two angle-driven shortcuts, ASA and AAS, by trying and failing to build a different triangle.
HL & why SSA/AAA fail
Two plausible-looking arrangements — two sides and a stray angle (SSA), and all three angles (AAA) — do NOT lock a triangle. Watch each one fail, and watch a single right angle rescue SSA. That rescue is exactly the HL criterion.
CPCTC & First Proofs
Once two triangles are congruent, every pair of corresponding parts is congruent — the skill is reading the correspondence, then using it as the last line of a proof.