Question

consider the diagram. the congruence theorem that can be used to prove △mnp ≅ △abc is
○ sss.
○ asa.
○ sas.
○ aas.

Explanation:

To determine the congruence theorem for \(\triangle MNP \cong \triangle ABC\), we analyze the given diagram (with markings for equal sides and angles):

1. Identify Equal Parts:

• From the diagram, we see two pairs of equal sides (marked with tick marks) and the included angle between them (marked with angle arcs) is equal (vertical angles or given congruent angles).
• The SAS (Side - Angle - Side) congruence theorem states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, the triangles are congruent.
• SSS requires three equal sides, ASA requires two angles and the included side, and AAS requires two angles and a non - included side. The markings here match the SAS criteria (two sides and the included angle).

Answer:

C. SAS