Given: KL = LM and

Question

warpedkitten · Answer

I believe it's Substitution and then AAS?

owlcoffee · Answer

not quite... When something is equal to itself, it's called "reflexive" property.
Now, you have two pairs of congruent angles and a pair of congruent sides.
Wich would be the property that'd allow you to conclude that the triangles are congruent?

warpedkitten · Answer

Would it be ASA?

owlcoffee · Answer

oh, wait. LJ is a segment of the triangle, so that would be two pairs of congruent sides and a pair of congruent angles.

warpedkitten · Answer

So then it would be SAS, not ASA?