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