Question

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

Explanation:

Step1: Apply the 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.
We need to check the proportion of the segments.
We have \(JK = 10\), \(KL=16\), \(LM = 24\), \(MN = 15\)
The proportion should be \(\frac{KL}{JK}=\frac{LM}{MN}\)

Step2: Calculate the ratios

Calculate \(\frac{KL}{JK}=\frac{16}{10}=\frac{8}{5}\)
Calculate \(\frac{LM}{MN}=\frac{24}{15}=\frac{8}{5}\)

Since \(\frac{16}{10}=\frac{24}{15}\)

Answer:

Yes, because \(\frac{16}{10}=\frac{24}{15}\) (The fourth option)