If two triangles have three congruent, corresponding angles, what additional information is needed to prove that the triangles are congruent?

Answer:

To prove that the triangles are congruent, you would need to know that at least one pair of corresponding side lengths is also congruent. Having congruent corresponding angles only proves that the triangles are similar. Once a pair of congruent corresponding sides is identified, the triangles can be proven congruent using the ASA (Angle-Side-Angle) or AAS (Angle-Angle-Side) congruence theorems.