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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?
Which statement can be proved true using the given theorem?


A) Segment BF = 9

B) Segment BD = 18

C) Segment BD = 20

D) Segment BF = 24

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 class=

Respuesta :

The values of BD and BF are respectively; 15 and 36

How to use line segment theorem?

We are given the line segment theorem which states that, a line that lies parallel to one side of a triangle will divide the other two lines proportionally.

Now, applying the given theorem to the given diagram, we can say that;

EF is parallel to AB as well as DE to BC

Thus;

AD/BD = AE/EC

Plugging in the relevant values gives;

18/BD = 24/20

Cross multiply to get;

BD = (20 * 18)/24

BD = 15

Similarly;

AE/EC = CF/BF

BF = CF * AE/CE

BF = (30 * 24)/20

BF = 36

Read more about Line segment theorem at; https://brainly.com/question/2437195

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Answer: C

Step-by-step explanation:

The triangle FEC is an Equilateral triangle so segment FE must be 20 as well and segment  FE and  BD and Parallel which makes it also 20




Hope this helps.

Sorry if it is wrong

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