Theorem: a line parallel to one side of a triangle divides the other two proportionately. in the figure below, segment de is parallel to segment bc and segment ef is parallel to ab:
which statement can be proved true using the given theorem?

a. segment bd = 12
b. segment bd= 4
c. segment bf= 16
d. segment bf= 9

C. Segment BF= 16

Step-by-step explanation:

Since the line EF cuts AD and BD proportionally, we can deduce the following:

We can then isolate BF, that way:

So, segment BF = 16.

We can also find segment BD the same way:

But BD = 9 isn't in the possible answers.

 The correct option is

(C) Segment BF = 16.

Step-by-step explanation:  We are given the following theorem :

"A line parallel to one side of a triangle divides the other two proportionately".

In the figure, segment DE is parallel to segment BC and segment EF is parallel to AB.

We are to select the statement that can be proved using the above theorem.

From the figure, we note that in triangle ABC,

AD = 6, AE = 12, CE = 18 and CF = 24.

Since DE is parallel to BC, so we get

Also, since EF is parallel to AB, so we get

Thus, the required true statement is BF = 16.

Option (C) is CORRECT.

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