Question

can you conclude that these triangles are congruent?

Explanation:

Step1: Check vertical angles

Vertical angles are equal. So, \(\angle HGJ=\angle M G K\)

Step2: Check side - side - side (SSS) or side - angle - side (SAS)

From the marks, \(HJ = MK\), \(HG=KG\), \(JG = MG\).
By the Side - Angle - Side (SAS) congruence criterion (two sides and the included angle).
In \(\triangle HJG\) and \(\triangle MKG\), \(HG = KG\), \(\angle HGJ=\angle M G K\), \(JG = MG\)

Answer:

yes