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.

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,

`(JM)/(MK)=(9)/(2)=4.5\\\\(JN)/(NL)=(11)/(3)=3.66666666667`

Thus,
`(JM)/(MK)\\eq(JN)/(NL)`

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

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