Question

which rule explains why these triangles are congruent? n m p k sss asa aas sas these triangles cannot be proven 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.
• ASA (Angle - Side - Angle): Two angles and the included side of one triangle are equal to the corresponding parts of another triangle.
• AAS (Angle - Angle - Side): Two angles and a non - included side of one triangle are equal to the corresponding parts of another triangle.
• SAS (Side - Angle - Side): Two sides and the included angle of one triangle are equal to the corresponding parts of another triangle.

Step2: Analyze the given triangles

• In \(\triangle NPK\) and \(\triangle KMN\), we have \(\angle P=\angle M\) (given as angles with the same marking), \(NP = KM\) (given as sides with the same marking), and \(NK=NK\) (common side).
• Here, we have two angles (\(\angle P\) and the right angle at \(K\) for \(\triangle NPK\), \(\angle M\) and the right angle at \(K\) for \(\triangle KMN\)) and a non - included side (\(NP = KM\)).

Answer:

AAS