Final answer:
To prove JL is greater than KL given JM≅MK, we assume these points are collinear with J, M, K, and L in order. A two-column proof can be formed, which uses given information, Segment Addition Postulate, substitution, and the fact that adding the same part ML to two segments with different lengths will preserve the inequality.
Step-by-step explanation:
To prove that JL is greater than KL given that JM≅MK, we can use a two-column proof structure. First, we need to make some assumptions about the points J, M, K, and L. Without loss of generality, let's assume that the points are collinear and J, M, K, and L are positioned in that order on a line.
Two-Column Proof
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- State that JM≅MK which is given.
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- Because JM is congruent to MK, they have the same length.
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- Stat that JL = JM + ML and KL = KM + ML, by the Segment Addition Postulate.
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- Since JM = MK from the earlier step, by substitution JL becomes JM + ML and KL becomes JM + ML.
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- JL > KL because JM is greater than KM since JL includes JM while KL includes the shorter segment KM.
This logical sequence of statements and reasons shows that JL must be greater than KL.