Question

which theorem is not a valid theorem to show that two triangles are congruent?
a. sas triangle congruence theorem
b. ssa triangle congruence theorem
c. asa triangle congruence theorem
d. aas triangle congruence theorem

Explanation:

Step1: Recall triangle congruence theorems

• SAS (Side - Angle - Side): If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent.
• ASA (Angle - Side - Angle): If two angles and the included side of one triangle are equal to two angles and the included side of another triangle, the triangles are congruent.
• AAS (Angle - Angle - Side): If two angles and a non - included side of one triangle are equal to two angles and the corresponding non - included side of another triangle, the triangles are congruent.
• SSA (Side - Side - Angle): This is not a valid congruence theorem in general. For example, consider two triangles where two sides and a non - included angle are equal. There can be two different triangles (an acute - angled and an obtuse - angled triangle) that satisfy the SSA condition but are not congruent.

Answer:

B. SSA Triangle Congruence Theorem