Question

which rule explains why these triangles are congruent?

Explanation:

Step1: Recall congruence rules

• SSS (Side - Side - Side): All three sides of one triangle are equal to the corresponding sides of another triangle.
• 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.
• ASA (Angle - Side - Angle): Two angles and the included side of one triangle are equal to the corresponding two angles and included side of another triangle.

Step2: Analyze the given triangles

• In \(\triangle MNK\) and \(\triangle PNK\), we have \(\angle M=\angle P\) (given as marked angles), \(NK = NK\) (common side), and \(MN=PN\) (marked as equal).
• The two angles (\(\angle M\) and \(\angle P\)) and a non - included side (\(NK\)) satisfy the AAS (Angle - Angle - Side) congruence rule.

Answer:

AAS