Question

with the information given in the diagram, which statement is not true?
the triangles can be proved by the asa theorem to be congruent.
the triangles can be proved by the aas theorem to be congruent.
the triangles can be proved to be congruent by using rigid motion to match them up exactly.
the triangles can be proved by the sss theorem to be congruent.

Explanation:

Step1: Recall triangle congruence theorems

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.
SSS (Side - Side - Side): If three sides of one triangle are equal to three sides of another triangle, the triangles are congruent.
Rigid motion: Transformations (translations, rotations, reflections) that preserve shape and size. If two triangles can be mapped onto each other using rigid motions, they are congruent.

Step2: Analyze the given diagram

From the diagram, we can see that we have two angles and a non - included side (AAS) congruent (by the markings of angles and sides). Also, rigid motion (since congruent triangles can be moved to match exactly). But for SSS, we do not have information about all three sides being marked as equal.

Answer:

The triangles can be proved by the SSS theorem to be congruent.