Question

which rule explains why these triangles are congruent? sss aas asa 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.
• 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.
• 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.
• 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.

Step2: Analyze the given triangles

In the two triangles \(\triangle KNM\) and \(\triangle JHG\), we have two sides (marked with one and two tick marks respectively) and the non - included angle (the angle not between the two marked sides) equal. This matches the AAS (Angle - Angle - Side) congruence rule.

Answer:

AAS