Congruent triangles
Two triangles are copies of each other. How do you say which parts match, and how few matching parts does it take to be sure?
Where you are 3 inside
What this area is about
Two triangles are congruent when their vertices can be matched so that all six pairs of parts, three sides and three angles, are congruent. Six checks is a lot. This area is about writing the matching down, and which shorter lists of matching parts do, or do not, force one.
How these fit together
Notation. Congruence statements and correspondence: letter order packs the matching, so \triangle ABC \cong \triangle DEF pairs A with D, B with E and C with F.
Short lists. The criteria sit next door: SSS, SAS and ASA are postulates, and AAS is a theorem from ASA and the Third Angle Theorem. Why AAA and SSA fail covers the other two: three angles fix the shape but not the size, and two sides with an angle not between them can build two different triangles. Hypotenuse leg congruence is the right-angle case of SSA, which is safe: a theorem for right triangles, proved from the Pythagorean theorem and SSS.
Using a congruence. Once two triangles are congruent, every matched part is, including pairs nobody checked. That fact lives with the proofs, in proving parts congruent after the triangles.
A path through it
Congruence statements first, then the criteria next door. Then why AAA and SSA fail, and last hypotenuse leg congruence, best read once you have seen SSA fail.
Finish here and you can prove triangles congruent, and then use it to prove sides and angles equal. The AAA lesson points on to similarity, where same shape is enough.