Question

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

Explanation:

Step1: Recall congruence criteria

For triangles, having three congruent corresponding angles (AAA) is not enough to prove congruence as the triangles can be similar but not congruent. We need information about side - lengths.

Step2: Identify needed side - length info

One of the following side - length related criteria can be used: Side - Angle - Side (SAS), Angle - Side - Angle (ASA), Side - Side - Side (SSS), Angle - Angle - Side (AAS). Since we already have the angles, we need at least one pair of corresponding congruent sides.

Answer:

One pair of corresponding congruent sides.