Before you write a proof, draw the figure and then plan what you will do to complete the proof.
From the figure, note that if you show HK = KL and JK = KM you have two sets of sides congruent.
Angles HKJ and LKM are vertical angles, and vertical angles are congruent and thus, by definition, equal.
Now you have SAS which shows triangle HKJ and LMK are congruent.
Now write the formal proof from the steps.
K is midpoint of HL and MJ --- Given
HK = KL and MK = KJ --- definition of midpoint
HK is congruent to KL and MK congruent KJ ---- Definition of congruent
HKJ and LKM are vertical angles ---- definition of vertical angles
measure of HKJ = measure LKM ----- vertical angle measure theorem
HKJ congruent LKM ---- definition of congruent
Triangle HKJ and Triangle LMK are congruent----SAS
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