Question

triangle mnp and triangle jkl are similar right triangles.
which proportion can be used to show that the slope of \\( \overline { j l } \\) is equal to the slope of \\( \overline { m p } \\)?

Explanation:

Step1: Recall the slope formula

The slope formula is \(m = \frac{\text{rise}}{\text{run}}\). For a right - triangle, the slope of a line segment (hypotenuse) can be represented as the ratio of the length of the vertical side (rise) to the length of the horizontal side (run) of the right - triangle.
For \(\overline{JL}\), if we consider the right - triangle \(JKL\), the slope \(m_{JL}=\frac{KL}{JK}\). For \(\overline{MP}\), if we consider the right - triangle \(MNP\), the slope \(m_{MP}=\frac{NP}{MN}\).
Since \(\triangle MNP\sim\triangle JKL\), the ratios of their corresponding sides are equal.

Answer:

\(\frac{KL}{JK}=\frac{NP}{MN}\)