Question

each option lists a combination of congruent parts between two triangles. classify each relationship as a triangle congruence theorem or a non - example of a triangle congruence theorem. > move each relationship into its category. triangle congruence theorem not a triangle congruence theorem sas asa ssa aaa sss

Explanation:

• SAS (Side - Angle - Side): If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, the triangles are congruent. This is a valid congruence theorem.
• ASA (Angle - Side - Angle): If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, the triangles are congruent. This is a valid congruence theorem.
• SSS (Side - Side - Side): If three sides of one triangle are congruent to three sides of another triangle, the triangles are congruent. This is a valid congruence theorem.
• SSA (Side - Side - Angle): Knowing two sides and a non - included angle does not guarantee triangle congruence. For example, there can be two different triangles (one acute and one obtuse) with the same SSA measurements. So, it is not a congruence theorem.
• AAA (Angle - Angle - Angle): Knowing three angles only tells us that the triangles are similar (same shape, but not necessarily the same size). So, it is not a congruence theorem.

Answer:

• Triangle Congruence Theorem: SAS, ASA, SSS
• Not a Triangle Congruence Theorem: SSA, AAA