Question

which triangle congruence theorem can be used to prove the triangles are congruent?

Explanation:

Step1: Recall triangle congruence theorems

• \(AAS\) (Angle - Angle - Side): Two angles and a non - included side of one triangle are equal to the corresponding two angles and non - included side of another triangle.
• \(SAS\) (Side - Angle - Side): Two sides and the included angle of one triangle are equal to the corresponding two sides and included angle of another triangle.
• \(SSA\) (Side - Side - Angle): This is not a valid congruence theorem in general (except for right - angled triangles where it is equivalent to \(HL\)).
• \(SSS\) (Side - Side - Side): Three sides of one triangle are equal to the three sides of another triangle.

Step2: Analyze the given figure

• In the given figure, we have two triangles. The two triangles have two pairs of equal sides (marked with tick marks) and the vertical angles (which are equal). The vertical angles are the included angles for the two pairs of equal sides.

Answer:

\(SAS\)