Question

which rule explains why these triangles are congruent? aas asa sss sas these triangles cannot be proven congruent.

Explanation:

Step1: Recall triangle congruence rules

• 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.
• SSS (Side - Side - Side): All three sides of one triangle are equal to the corresponding three sides 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 \(\triangle QKP\) and \(\triangle NKM\), \(\angle Q=\angle N\) (given), \(\angle P=\angle M\) (given), and \(\angle QKP=\angle NKM\) (vertically opposite angles).
• The side is not included between the two given angles.

Answer:

AAS