Question

which rule explains why these triangles are congruent? triangles qnp and kjm with markings options: aas, sss, sas, asa, these triangles cannot be proven congruent.

Explanation:

Step1: Analyze triangle markings

In $\triangle NQP$ and $\triangle KJM$: One side is marked congruent (the tick marks), one pair of angles (the single arc) and another pair of angles (the double arc) are congruent. The arrangement is two angles and a non - included side (AAS: Angle - Angle - Side) because the side is not between the two angles.

Step2: Match with congruence rules

• SSS (Side - Side - Side) requires three sides congruent, which is not the case here.
• SAS (Side - Angle - Side) requires two sides and the included angle, not the case here.
• ASA (Angle - Side - Angle) requires the side to be between the two angles, which is not the case here.
• AAS (Angle - Angle - Side) fits as we have two angles and a non - included side congruent.

Answer:

AAS