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D 8. (05.01 MC)
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:
A
6
12
D
18
B
F
24
Which statement can be proved true using the given theorem? (6 points)
O Segment BF = 16
O Segment BF - 9
Segment BD = 4
O Segment BD - 12

D 8 0501 MC 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 class=

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Answer:

hello i believe the answer is 16

Step-by-step explanation:

im in flvs and im doing the test right now

akposevictor

Using the theorem, the statement that can be proved to be true is:

A. Segment BF = 16

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

Using this theorem and the diagram given:

EF is parallel to AB as well as DE to BC

Therefore:

[tex]\frac{AB}{BD} = \frac{AE}{EC}[/tex]

  • Substitute

[tex]\frac{6}{BD} = \frac{12}{18} \\\\BD = \frac{6 \times 18}{12} \\\\\mathbf{BD = 9}[/tex]

Also:

[tex]\frac{CE}{AE} = \frac{CF}{BF} \\\\[/tex]

  • Substitute

[tex]\frac{18}{12} = \frac{24}{BF} \\\\BF = \frac{24 \times 12}{18} \\\\\mathbf{BF = 16}[/tex]

Therefore, using the theorem, the statement that can be proved to be true is:

A. Segment BF = 16

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https://brainly.com/question/17177615

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