Is KM||JN? Explain your reasoning.

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.

Cancel the common factors, we get

Similarly,

Cancel the common factors, we get

Therefore KM is not parallel to JN.