GEOMETRY: Determine whether segment MN is parallel to segment KL. Justify your answer. See attachment above (JM: 9, MK:2, JN: 11, NL: 3)Thanks so much to whoever answers this. I've been struggling for 30 minutes. :0)

Accepted Solution

Answer: segment MN is not parallel to segment KL.Step-by-step explanation:Converse of basic proportionality theorem says that if a line divides any two sides of a triangle in the same ratio, then the line must be parallel to the third side.Given: In triangle JKL, where line segment MN is dividing JK and Jl at M and N respectively.Now, [tex]\frac{JM}{MK}=\frac{9}{2}=4.5\\\\\frac{JN}{NL}=\frac{11}{3}=3.66666666667[/tex]Thus, [tex]\frac{JM}{MK}\neq\frac{JN}{NL}[/tex]β‡’ segment MN is not parallel to segment KL [by converse of basic proportionality theorem]]