It seems there are always three pairs: SSS, side side side; SAS, side angle side; ASA, angle side angle.
For a right triangle (HL, LL) it seems there are only two items needed, but that's because we already know one angle (it's right).
Once we have congruent triangles, all the corresponding parts are congruent. That's three sides and and three vertices, so I'd answer six. Of course almost everything about the triangles is the same, the area, the perimeter, etc.
