Question

Is KM||JN? Explain your reasoning.

Answer 1

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.

Answer 2

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.

`$\Rightarrow (LK)/(KJ) = (18)/(10)`

Cancel the common factors, we get

`$\Rightarrow (LK)/(KJ) = (9)/(5)`

Similarly,

`$\Rightarrow (LM)/(MN) = (24)/(15)`

Cancel the common factors, we get

`$\Rightarrow (LM)/(MN) = (8)/(5)`

`$(9)/(5)\\eq (8)/(5)`

`$\Rightarrow (L K)/(K J) \\eq (L M)/(M N)`

Therefore KM is not parallel to JN.