Question

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:
27
C
Which statement can be proved true using the given theorem?
Segment BD 32
Segment BD = 36
Segment BF = 15
Segment BF = 18

Answer 1

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