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

Answer 1

So when we have a line that is parallel to one side in a triangle, then that means it divides the other two sides proportionally

Answer 2

This means that since DE is parallel to side BC we get

\(\dfrac{AD}{AB} = \dfrac{AE}{AC}\)

or also

\(\dfrac{AD}{DB} = \dfrac{AE}{EC}\)


and since we also have side EF parallel to AB, we get
\(\dfrac{AE}{AC} = \dfrac{BF}{BC}\)

or

\(\dfrac{AE}{EC} = \dfrac{BF}{FC}\)

Answer 3

@AZ

Answer 4

what does that mean

Answer 5

The sides are proportional. The two letters just means that line between those two points

Answer 6

So let's just use one of these

\( \dfrac{AD}{DB} = \dfrac{AE}{EC}\)

From your image, you can see that
AD = 16
DB = ??
AE = 24
EC = 36

Can you plug it in and solve for DB?

Answer 7

ill try

Answer 8

just replace it with the numbers

and in place of DB, you can use `x` and then we solve for x :)

Answer 9

Good! Let's just put an x there and solve for it

Answer 10

what would i have to do to find X

Answer 11

oo of course

we would cross multiply

Answer 12

so when we do that, we get

16 * 36 = x * 24

can you solve for x now?

Answer 13

i got 76

Answer 14

something isnt right

Answer 15

mhmm try again

what is 16*36 = ?
and then divide by 24

Answer 16

when i do that i get 72 and 24 can go into 72

Answer 17

I'm not sure how you're getting 72 or 76

Let's simplify the numbers first, shall we?

Answer 18

I just simplified the fraction

so now what is

3 * 16 = 2 * x

Answer 19

im doing my math wrong
i got zero

Answer 20

okay okay, step by step

just pull out the calculator

what is 16 * 3 = ?

Answer 21

48

Answer 22

now divide by 2

48/2 = ?

Answer 23

24

Answer 24

so we get x = 24

and we said x was the line segment BD

and since that isn't an answer choice that means we have more work to do and we have to figure out what line segment BF is

Answer 25

oh lord

Answer 26

I know right?!

Answer 27

math is alot

Answer 28

So from the proportions I wrote earlier, we have to use this one now

\(\dfrac{AE}{EC} = \dfrac{BF}{FC}\)

Answer 29

so now we're solving for BF (because the two remaining answer choices and that's also the only side we don't know yet)

From your main image
AE = 24
EC = 36
BF = ??
FC = 27

so can you carry it away from here now? o:

Answer 30

@AZ

Answer 31

it it 18

Answer 32

You got it!

Answer 33

i had too look back at everthing srry

Answer 34

That's fine! I'm glad you finally got it :)

Answer 35

thank you

Answer 36

You're welcome!