Do you think there is a postulate or theorem for aas, aaa, or ssa congruence? why or why not?

there is an aas congruence theorem (not postulate) since it's a statement that needs to be proven, and it can be proven. there is no aaa congruence theorem, but there is an aaa similarity theorem. though we only need 2 angles so it reduces to aa similarity. if your teacher is only looking for congruence theorems, then you can cross aaa off the list. there is no such thing as ssa congruence as this leads to a possibility of (1) having two triangles, or (2) having one triangle, or (3) having no triangles at all. with congruence theorems, we need to have exactly one tangle possible.

in short, there is only one theorem you listed and it is the aas congruence theorem. note: we can solve or the missing angle and use a similar theorem asa