Question

Determine whether JK is parallel to MN. Show your work.

Answer 1

Let's put the given details in the figure to better understand the scenario.

For JK and MN to be proven parallel, the following relationship of sides must satisfy:

`\text{ }\frac{\text{ JN }}{\text{JL}}\text{ = }\frac{\text{ KM }}{\text{KL}}`

This relationship of sides is under the Triangle Proportionality Theorem.

Under this theorem, if a line parallel to one side of a triangle intersects the other two sides, then it divides those sides proportionally.

Let's now investigate,

JN = 18

JL = 30

KM = 21

KL = 56

We get,

`\text{ }(18)/(30)\text{ = }(21)/(56)`
`\text{ }(3)/(5)\text{ = }(3)/(8)\text{ \lparen Simplified form\rparen}`
`\text{ 3 x 8 = 3 x 5}`
`\text{ 24 }\\e\text{ 15}`

From our investigation, it appears that the sides aren't proportional.

Therefore, JK and MN are not parallel.