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Langali · Answer 1 · 2024-07-21T20:59:35+0000

The two-column proof that proves
$(m\angle LMK > m\angle MKN)$ this is that the angle opposite the longer side (LK) is larger than the angle opposite the shorter side (MN).

Given that
$(KN \cong LM) and (LK > MN)$ , we need to prove that
$(m\angle LMK > m\angle MKN)$ .

Here is the two-column proof:

Statement 1:
$(KN \cong LM)$ (Given) Reason: Given

Statement 2:
(LK > MN) (Given) Reason: Given

Statement 3:
$(m\angle LMK > m\angle MKN)$ Reason: In a triangle, if one side is longer than another, the angle opposite the longer side is larger. This is a property of triangles.

This completes the proof. The angle opposite the longer side (LK) is larger than the angle opposite the shorter side (MN).

Thus, from the two-column proof, we can conclude that
$(m\angle LMK > m\angle MKN)$ .

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