Let's start with the information given:
- KJ and MJ are congruent.
- m∠K and m∠M are congruent.
We don't have another clear information, but we need one more to use one of the methods.
As we can see, the interior angles at vertex J are opposite, that is, they are Vertical Angles. Vertical Angles are congruent, so we have one more information:
- m∠HJM and m∠LJK are congruent.
Thus, we have an Angle congruence, a side congruence and another angle congruence, so this can use the Angle-Side-Angle method to prove the congrunce of the triangles.
That is, the methos is Angle-Side-Angle (ASA).