Question

HELP!

Answer 1

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,

$\frac{3}{2}{\neq}\frac{7}{4}$

Hence, The line segment LN is not parallel to XY.

Answer 2

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