Given:
JK = 10, LK = 18, MN = 15 and LM = 24
To find:
The segment KM is parallel to JN or not.
Solution:
Converse of the triangle proportionality theorem:
If a line divides two sides of a triangle proportionally, then it is parallel to the third side.
[tex]$\Rightarrow \frac{LK}{KJ} = \frac{18}{10}[/tex]
Cancel the common factors, we get
[tex]$\Rightarrow \frac{LK}{KJ} = \frac{9}{5}[/tex]
Similarly,
[tex]$\Rightarrow \frac{LM}{MN} = \frac{24}{15}[/tex]
Cancel the common factors, we get
[tex]$\Rightarrow \frac{LM}{MN} = \frac{8}{5}[/tex]
[tex]$\frac{9}{5}\neq \frac{8}{5}[/tex]
[tex]$\Rightarrow \frac{L K}{K J} \neq \frac{L M}{M N}[/tex]
Therefore KM is not parallel to JN.
