Question

in the figure shown, which theorem can be used to show that \\( \triangle abc \cong \triangle 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

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

Step2: Analyze the given triangles

In \(\triangle ABC\) and \(\triangle DEF\), we have two pairs of angles (\(\angle B\cong\angle E\), \(\angle A\cong\angle D\)) and a pair of non - included sides (the marked sides) congruent. This matches the AAS (Angle - Angle - Side) Triangle Congruence Theorem.

Answer:

C. AAS Triangle Congruence Theorem