Question

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 DF. Point D is on side AB, point E is on side AC and point F is on side BC. Segment AD is 16, segment AE is 24, segment EC is 36, and segment FC is 27

Which statement can be proved true using the given theorem?

Segment BD = 32

Segment BD = 36

Segment BF = 15

Segment BF = 18

@Nurali @zepdrix @Compassionate

Answer 1

I put the first one as the answer but I just want to make sure I'm correct.

Answer 2

i think BF=18

Answer 3

the big triangle ABC is similar to both triangles ADE and EFC

Answer 4

DEBF is a parallelogram (sides are parallel) so you know side BD = EF
and side BF= DE

Answer 5

because both "little" triangles ADE and EFC are similar, you can set up ratios of side to side and solve for the unknown side

Answer 6

for example, to find BD, we solve for EF (which is part of a triangle)

\[ \frac{EF}{36} = \frac{16}{24} \]

Answer 7

So I need to cross multiply that to find my answer?

Answer 8

I would first simplify 16/24 to ⅔ (divide top and bottom by 8)
to make it a simpler problem

Answer 9

Okay lemme do that real quick and I'll tell you what I get.

Answer 10

http://sketchtoy.com/62537891

Answer 11

is that right?

Answer 12

yes, and because BD= EF (opposite sides of a parallelogram are equal)
BD= 24

Answer 13

Thanks :)

Answer 14

Waaaitt. I dont have that in my multiple choice.

Answer 15

that means the first two choices are not the answer.
you have to find side BF, which is the same as side DE
write a ratios of top right side to bottom side

Answer 16

Like set them up to cross multiply?

Answer 17

yes

Answer 18

ok one min

Answer 19

Which numbers am i using?

Answer 20

you look at the little triangle at the top. you have to use side DE (because that is the one you are solving for), and one other side.

to figure out which, look at the little triangle on the right with sides 36 and 27
the 27 (the bottom) "goes with" DE (the bottom of the first triangle)
the 36 will go with the "same side" of the first triangle (labeled 24)

Answer 21

I say to myself: bottom side triangle one / top right side of triangle one
equals
bottom side triangle two / top right side of triangle two

Answer 22

So I know one is 36/27 but what goes under DE?

Answer 23

or 27/36, either one

Answer 24

if you pick 36/27 (which you should simplify)

look at the triangle. 36 is the top right side
and 27 is the bottom side

that means you write another ratio using the other triangle, *in the same order*
top right side divided by bottom side

what is the other ratio?

Answer 25

24/DE?

Answer 26

exactly
set the two ratios equal
36/27 = 24/DE

but simplify 36/27 (divide top and bottom by 9)

Answer 27

4/3 = 24/DE

Answer 28

18!! thanks for helping me

Answer 29

yw