Question

can you conclude that these triangles are congruent?
yes \t\t no

Explanation:

Step1: Identify given congruences

We know \( \angle J \cong \angle N \) (marked angles), \( JH \cong NH \) (marked segments), and \( \angle JHK \cong \angle NHM \) (vertical angles are congruent).

Step2: Apply ASA congruence criterion

The Angle - Side - Angle (ASA) congruence postulate states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent. For \( \triangle JHK \) and \( \triangle NHM \), we have \( \angle J\cong\angle N \), \( JH = NH \), and \( \angle JHK\cong\angle NHM \). So by ASA, \( \triangle JHK\cong\triangle NHM \).

Answer:

yes