Which of the following is NOT one of the Triangle Congruence Theorems?

Which of the following is NOT one of the Triangle Congruence Theorems?

• A. SSS
• B. ASA
• C. AAA
• D. SAS

Answer: (C)

The Triangle Congruence Theorems are the criteria used to determine whether two triangles are congruent, meaning they have the same shape and size. The three valid criteria that establish congruence are: - Side-Side-Side (SSS): If the lengths of all three sides of one triangle are equal to the lengths of all three sides of another triangle, then the triangles are congruent. - Side-Angle-Side (SAS): If two sides of one triangle are equal to two sides of another triangle and the included angle between those sides is equal, then the triangles are congruent. - Angle-Side-Angle (ASA): If two angles and the side between them in one triangle are equal to the corresponding parts in another triangle, then the triangles are congruent. The Angle-Angle-Angle (AAA) criterion, while it can show that two triangles have the same shape (similarity), does not establish congruence. AAA does not guarantee that the triangles are of the same size; instead, it indicates that the triangles are similar, meaning they have the same angles, but their sides may differ in length. Thus, AAA cannot confirm triangle congruence in the same way SSS,

The Triangle Congruence Theorems are the criteria used to determine whether two triangles are congruent, meaning they have the same shape and size. The three valid criteria that establish congruence are:

• Side-Side-Side (SSS): If the lengths of all three sides of one triangle are equal to the lengths of all three sides of another triangle, then the triangles are congruent.

• Side-Angle-Side (SAS): If two sides of one triangle are equal to two sides of another triangle and the included angle between those sides is equal, then the triangles are congruent.

• Angle-Side-Angle (ASA): If two angles and the side between them in one triangle are equal to the corresponding parts in another triangle, then the triangles are congruent.

The Angle-Angle-Angle (AAA) criterion, while it can show that two triangles have the same shape (similarity), does not establish congruence. AAA does not guarantee that the triangles are of the same size; instead, it indicates that the triangles are similar, meaning they have the same angles, but their sides may differ in length. Thus, AAA cannot confirm triangle congruence in the same way SSS,