Question

MEDAL + FAN!!
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?
A. Segment BF = 9
B. Segment BD = 18
C. Segment BD = 20
D. Segment BF = 24

Answer 1

What do you think it is?

Answer 2

@dan815 @mathmate

Answer 3

18

Answer 4

Is the "given theorem" the intercept theorem (or Thales theorem)?
Hint: the following link will lead you to the solution:

http://planetmath.org/intercepttheorem

Answer 5

thanks

Answer 6

you're welcome! :)

Answer 7

I dont get it :/

Answer 8

Sorry, the above link did not seem to work. This is the correct one:
http://math.stackexchange.com/questions/92929/similar-triangle-theorem-in-the-incommensurable-case

I'll give you an example:

The intercept theorem says
AD/DB = AE/EC
Substituting AD=5, AE=4, EC=3, we have
5/x=4/3
cross multiply to get
15=4x
solving gives
x=15/4.

Answer 9

ok thanks!

Answer 10

You're welcome! :)