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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:

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 :

viginiengum

Answer: Segment BF = 16

Step-by-step explanation:

weaverbyron315

Answer: Segment BD = 15

Step-by-step explanation: Ok. So, we know that segment DE is parallel to segment BC and segment EF is parallel to segment AB. The triangle proportionality theorem states that if a line is parallel to one side of a triangle and also intersects the other two sides, the line divides the sides proportionally. To put it more simply; because segment EF is parallel to segment AB, triangles ADE and EFC are proportional and similar. From there we must find the scale factor by which these two triangles are proportional.

We can do this by dividing the corresponding segments by; each other.

24 ÷ 20 = 1.2

Scale Factor = 1.2

Then we divide segment AD (18) by the scale factor (1.2).

18 ÷ 1.2 = 15

Since segment EF is parallel to segment AB, segment EF corresponds and is congruent to segment DB.

So,

Segment BD = 15

I also got it right on the test, soooo.... yeah

Thar ya go

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