Question

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)

Answer 1

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,

$\frac{JM}{MK}=\frac{9}{2}=4.5\\\\\frac{JN}{NL}=\frac{11}{3}=3.66666666667$

Thus, $\frac{JM}{MK}\neq\frac{JN}{NL}$

⇒ segment MN is not parallel to segment KL [by converse of basic proportionality theorem]

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