Question

which rule explains why these triangles are congruent? sss aas sas asa 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.
• 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.
• ASA (Angle - Side - Angle): Two angles and the included side of one triangle are equal to the corresponding parts of another triangle.

Step2: Analyze the given triangles

• In \(\triangle NPM\) and \(\triangle QMP\), we have \(NP = QM\) (marked with one tick), \(\angle NPM=\angle QMP\) (marked angles), and \(PM = PM\) (common side).

Step3: Match with the congruence rule

• The given information matches the SAS (Side - Angle - Side) rule as we have two sides (\(NP = QM\) and \(PM = PM\)) and the included angle (\(\angle NPM=\angle QMP\)) equal.

Answer:

SAS