Question

is \\( \overline { k m } \parallel \overline { j n } \\) ? 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 Basic Proportionality Theorem (Thales' Theorem)

If a line divides two sides of a triangle proportionally, then it is parallel to the third side. For \(\triangle LJN\), we check if \(\frac{LK}{KJ}=\frac{LM}{MN}\).
Here, \(LK = 16\), \(KJ=10\), \(LM = 24\), \(MN = 15\).
We calculate \(\frac{LK}{KJ}=\frac{16}{10}=\frac{8}{5}\) and \(\frac{LM}{MN}=\frac{24}{15}=\frac{8}{5}\).

Answer:

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