Question

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

Explanation:

Step1: Identify given congruent parts

We have \( NH = JH \) (marked with two ticks), \( NM = JK \) (marked with one tick), and \( \angle NHM \) and \( \angle JHK \) are vertical angles, so \( \angle NHM=\angle JHK \).

Step2: Match with congruence rules

The SAS (Side - Angle - Side) congruence rule states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent. Here, we have two sides (\( NH = JH \), \( NM = JK \)) and the included angle (vertical angles, hence equal) between them. So the triangles \( \triangle NHM \) and \( \triangle JHK \) are congruent by SAS.

Answer:

SAS