Question

which similarity theorem can be used to prove that the triangles are congruent? use capital letters and type the theorem. answer attempt 2 out of 2

Explanation:

Similarity theorems for triangles include AA (Angle - Angle), SAS (Side - Angle - Side), SSS (Side - Side - Side). If two angles of one triangle are equal to two angles of another triangle, AA similarity is used. If the ratios of two pairs of corresponding sides are equal and the included angles are congruent, SAS similarity applies. When the ratios of all three pairs of corresponding sides are equal, SSS similarity is used. However, similarity does not imply congruence directly. But if we consider the special - case where the ratio of similarity is 1 (i.e., the corresponding sides are equal in length), then the SSS, SAS, ASA (Angle - Side - Angle), AAS (Angle - Angle - Side) and HL (Hypotenuse - Leg for right - triangles) congruence theorems can be used. Since the question asks for a similarity theorem that can lead to congruence, when the similarity ratio is 1, SSS similarity becomes SSS congruence, SAS similarity becomes SAS congruence etc.

Answer:

SSS, SAS, AA (Note: AA similarity alone does not prove congruence without additional information about side - lengths, but in the context of similarity theorems in general, it is listed. For congruence, SSS and SAS from the similarity perspective with a ratio of 1 are more directly applicable in terms of the similarity - congruence connection)