Final answer:
Given that KN ≅ LM and LK > MN, we deduce that m∠LMK is greater than m∠MKN because in a triangle, larger sides oppose larger angles. This conclusion does not rely on any of the standard congruence postulates (SAS, AAS, SSS, ASA) as they are for triangle congruence, not angle comparison.
Step-by-step explanation:
The question involves comparing the measures of two angles in a triangle. To prove that m∠LMK is greater than m∠MKN, we can use the information given: KN ≅ LM and LK > MN. The information provided suggests that side LK is not just longer than side MN, but also serves as the side of angle LMK which would make angle LMK greater than angle MKN due to the property that in any triangle, greater sides oppose greater angles.
None of the answer choices A) SAS, B) AAS, C) SSS, D) ASA directly apply to this proof as they are all methods for proving triangle congruence, and here we are not proving triangles congruent, but rather comparing the sizes of two angles based on the given side lengths. The correct reasoning comes from understanding triangle inequality and the fact that larger sides oppose larger angles within a triangle.