Question

practice applying the side-splitter theorem, its converse and the triangle midsegment theorem. is \\(\overline{km} \parallel \overline{jn}\\)? why or why not? \\(\bigcirc\\) no, because \\(\frac{16}{10} \
eq \frac{24}{15}\\). \\(\bigcirc\\) yes, because \\(\frac{10}{24} = \frac{15}{16}\\). \\(\bigcirc\\) yes, because \\(\frac{16}{10} = \frac{15}{24}\\) \\(\bigcirc\\) yes, because \\(\frac{16}{10} = \frac{24}{15}\\).

Explanation:

Step1: Recall converse of side-splitter theorem

If a line divides two sides of a triangle proportionally, it is parallel to the third side.

Step2: Identify segment ratios

Check $\frac{LK}{KJ}$ and $\frac{LM}{MN}$: $\frac{16}{10} = 1.6$, $\frac{24}{15} = 1.6$.

Step3: Compare ratios

$\frac{16}{10} = \frac{24}{15}$, so KM || JN.

Answer:

Yes, because $\frac{16}{10} = \frac{24}{15}$.