OddballCat13
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PLEASE HELP ME!
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:

The figure shows triangle ABC with segments DE and EF. Point D is on side AB, point E is on side AC, and point F is on side BC. Segment AD is 18, segment AE is 24, segment EC is 20, and segment FC is 30.

Which statement can be proved true using the given theorem?

Segment BF = 16
Segment BD = 20
Segment BD = 15
Segment BF = 32

Respuesta :

sqdancefan

Answer:

  (c)  Segment BD = 15

Step-by-step explanation:

You have ∆ABC with ∆DEF inscribed so that DE║BC, EF║AB, and points D, E, and F lie on segments AB, AC, and BC, respectively. You want to know the lengths of BF and BD, given that AD=18, AE=24, EC=20, FC=30.

Proportions

The parallel lines divide the triangle sides proportionally, so we have ...

  BD/AD = CE/AE

  BD/18 = 20/24 . . . . . using the given values

  BD = 18(20/24) = 15

On the other side, we have ...

  BF/CF = AE/CE

  BF/30 = 24/20

  BF = 30(24/20) = 36 . . . . . not among the answer choices

The length of interest is ...

  Segment BD = 15.

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