Which of the following is not a criterion for triangle congruence?

The criterion for triangle congruence focuses on methods to determine whether two triangles are congruent, meaning they are identical in shape and size, regardless of their orientation. The options Side-Angle-Side (SAS), Side-Side-Side (SSS), and Angle-Side-Angle (ASA) are all valid methods for proving triangle congruence, as they provide sufficient information to ensure that two triangles are identical.

On the other hand, Angle-Angle-Angle (AAA) is not considered a criterion for triangle congruence because, while it indicates that two triangles have the same shape (same angles), it does not provide information about the triangles’ size. Thus, two triangles could be similar (same shape but different sizes) without being congruent. In other words, having equal angles does not guarantee that the lengths of the corresponding sides are equal, which is essential for congruence. Therefore, it is the AAA criterion that does not apply to the concept of triangle congruence, making it the correct choice in this context.