Answer:
Step-by-step explanation:
The two lines are parallel in the triangle if they satisfy the basic proportionality theorem that is:
[tex]\frac{MX}{XL}=\frac{MY}{YN}[/tex]
Now, different segments lengths are given as:
(A) LX=2, XM=7, NY=4 and YM=14
Applying the basic proportionality theorem,
[tex]\frac{7}{2}=\frac{14}{4}[/tex]
[tex]\frac{7}{2}=\frac{7}{2}[/tex]
Hence, The line segment LN is parallel to XY.
(B) LX=2, XM=6, NY=3 and YM=9
Applying the basic proportionality theorem,
[tex]\frac{6}{2}=\frac{9}{3}[/tex]
[tex]\frac{3}{1}=\frac{3}{1}[/tex]
Hence, The line segment LN is parallel to XY.
(C) LX=2, XM=3, NY=4 and YM=7
Applying the basic proportionality theorem,
[tex]\frac{3}{2}{\neq}\frac{7}{4}[/tex]
Hence, The line segment LN is not parallel to XY.
