Question

in the figure shown, which theorem can be used to show that △abc≅△def?
a. the triangles are not congruent.
b. sas triangle congruence theorem
c. aas triangle congruence theorem
d. asa triangle congruence theorem

Explanation:

Step1: Recall triangle congruence theorems

• ASA (Angle - Side - Angle): Two angles and the included side of one triangle are equal to two angles and the included side of another triangle.
• AAS (Angle - Angle - Side): Two angles and a non - included side of one triangle are equal to two angles and the corresponding non - included side of another triangle.
• SAS (Side - Angle - Side): Two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle.

Step2: Analyze the given triangles

In \(\triangle ABC\) and \(\triangle DEF\), we have two angles (\(\angle A=\angle F\), \(\angle B=\angle E\)) and a non - included side (the side marked with one tick mark). This matches the AAS (Angle - Angle - Side) congruence theorem.

Answer:

C. AAS Triangle Congruence Theorem