Question

Help me pls! It would help me a lot. This is also worth 30 points!!!!

Answer 1

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)`.