Question

which theorem could be used to prove \\( \triangle abd \cong \triangle dca \\)?

choose the correct answer below.

sss

sas

aas

aaa

Explanation:

Step1: Recall triangle congruence theorems

• SSS (Side - Side - Side): If three sides of one triangle are equal to three sides of another triangle, the triangles are congruent.
• 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.
• 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.
• AAA (Angle - Angle - Angle) only shows similarity, not congruence.

Step2: Analyze the given triangles

In \(\triangle ABD\) and \(\triangle DCA\), we have two pairs of angles (as shown in the figure) and a common side \(AD = DA\) (non - included side for the two pairs of angles).

Answer:

C. AAS