Answer:
AAA and SSA.
Step-by-step explanation:
The triangle congruence theorems that we have involving the sides and angles of a triangle are:
SSS (side-side-side);
SAS (side-angle-side);
AAS (angle-angle-side); and
ASA (angle-side-angle).
If we had AAA, angle-angle-angle, all we would be able to prove is that the triangles are similar. This does not prove congruence.
If we had SSA, side-side-angle, it will only work sometimes. If the side which lies on one ray of the angle is shorter than the other side (not on the ray of the angle), the two triangles will be of the same shape and size (congruent).
If the side which lies on one ray of the angle is longer than the other side, and the other side is the minimum distance needed to create a triangle(by the triangle inequality theorem), the two triangles will be congruent.
If the side which lies on one ray of the angle is longer than the other side, and the other side is greater than the minimum distance needed to create a triangle (by the triangle inequality theorem), the two triangles will not necessarily be congruent.
If the side which lies on one ray of the angle is longer than the other side, and the other side is less than the minimum distance needed to create a triangle (by the triangle inequality theorem), no triangle can be drawn. Since no triangles are possible, no congruent triangles are possible.
