Given triangles abc and def. which triangle congruence theorem can prove triangle abc congruent to triangle def? angle-side-angle (asa) side-angle-side (sas) side-side-side (sss) all of the above

The answer is: All of the above.

First, we need to know that both triangles have the same dimensions:

If two triangles have the same side length, the angles will be the same two.

Hence,

If both triangles have the same side length, they are congruent according to the Side-Side-Side(SSS) triangle congruence theorem. It also means that:

Both triangles have the same angles, meaning that its angles are congruent. If there is at least one angle which is congruent, and there are at least two sides that are equal for both triangles, the triangles are congruent according to the Side-Angle-Side (SAS) triangle congruence theorem.

If two angles and at least a side are congruent, the triangles are congruent. According to the Angle-Side-Angle(ASA), if two angles and the included side are congruent, the triangles are congruent.

For this case, each theorem will be satisfied because the triangles have the same side length, meaning that all of the above theorem can prove that the triangles ABC and DEF are congruent.

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