Question

based on the side-splitter theorem, which side length would complete the proportion? (\frac{jm}{mk} = \frac{ln}{?}) options: jl, kl, nk, nm (diagram: triangle with points j, l, k; m on jk, n on kl; jm and mn have parallel arrows)

Explanation:

Step1: Recall Side - Splitter Theorem

The Side - Splitter Theorem states that if a line is parallel to one side of a triangle and intersects the other two sides, then it divides those sides proportionally. In triangle \(JKL\), line \(MN\) is parallel to \(JL\) (since the arrows indicate parallel lines). So, \(\frac{JM}{MK}=\frac{LN}{NK}\) because \(MN\) divides \(JK\) into \(JM\) and \(MK\) and divides \(KL\) into \(LN\) and \(NK\) proportionally.

Answer:

C. NK