Answer
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Work Step by Step
According to the corollary to the side-splitter theorem, if three parallel lines cut through two transversals, then the segments on one transversal cut by the parallel lines are proportional to the segments on the other transversal cut by the parallel lines.
Now we can set up the proportions to compare the segments on one transversal to the segments on the other transversal. $\overline{QL}$ and $\overline{SQ}$ are two segments on one transversal; $\overline{PM}$ and $\overline{JP}$ are the first two segments on the other transversal. Let's set up the proportion for these segments:
$\frac{QL}{SQ} = \frac{PM}{JP}$
According to one of the properties of proportions, we can rewrite the proportion so that the means are switched:
$\frac{QL}{PM} = \frac{SQ}{JP}$
