Let's put the given details in the figure to better understand the scenario.
For JK and MN to be proven parallel, the following relationship of sides must satisfy:
[tex]\text{ }\frac{\text{ JN }}{\text{JL}}\text{ = }\frac{\text{ KM }}{\text{KL}}[/tex]
This relationship of sides is under the Triangle Proportionality Theorem.
Under this theorem, if a line parallel to one side of a triangle intersects the other two sides, then it divides those sides proportionally.
Let's now investigate,
JN = 18
JL = 30
KM = 21
KL = 56
We get,
[tex]\text{ }\frac{18}{30}\text{ = }\frac{21}{56}[/tex][tex]\text{ }\frac{3}{5}\text{ = }\frac{3}{8}\text{ \lparen Simplified form\rparen}[/tex][tex]\text{ 3 x 8 = 3 x 5}[/tex][tex]\text{ 24 }\ne\text{ 15}[/tex]
From our investigation, it appears that the sides aren't proportional.
Therefore, JK and MN are not parallel.
