Question

For which segment lengths is LN⎯⎯⎯⎯⎯ parallel to XY⎯⎯⎯⎯⎯ ?

For which segment lengths is LN⎯⎯⎯⎯⎯ parallel to XY⎯⎯⎯⎯⎯ ?
Select Parallel or Not parallel for each set of given information.
Segment lengths Parallel Not parallel
LX=2, XM=7, NY=4, YM=14 --- ----

LX=2, XM=6, NY=3, YM=9 --- -----

LX=2, XM=3, NY=4, YM=7 --- -----

Answer 1

Case 1 : XY Parallel to LN

Case 2 : XY Parallel to LN

Case 3 : XY Not Parallel to LN

Explanation:

Hope you refer to the above figure

If XY & LN are parallel, then the two triangles MLN & MXY are similar.

`:. (ML) / (MX) = (MN) / (MY) = (LN) / (XY)`

`(MX + LX) / (MX) = (MY + NY) / (MY)`

`cancel(1) + (LX)/(MX) = cancel(1) + (NY) / (MY)`

`(LX) / (MX) = (NY) / (MY)`

Substituting the values

Case 1 :
Given `LX =/2, XM = 7, NY = 4, YM = 14`

`2/7 = 4/14 = 2/7` satisfies the condition that XY // to LN

Case 2 :
Given `LX = 2, XM = 6, NY = 3, YM = 9`

`2/6 = 3/9 = 1/3` satisfies the condition that XY // to LN

Case 3 :

Given `LX = 2, XM = 3, NY = 4, YM = 7`

`2/3 != 4/7` does not satisfy the similarity condition and hence

XY not // to LN