Question

Help?

Answer 1

I think it's 90.

Answer 2

I don't know the answer yet.

The theorem at work here is this:

If a line is parallel to one side of a triangle and intersects the other two, then it divides them proportionally.

That theorem will be used twice to get the two sides.

Answer 3

Yeah, it's 108

Answer 4

Thank you! :)

Answer 5

Look on the attachment for an equation to solve.

Answer 6

@Annetta_Martin Are you saying that you have solved this problem?

Answer 7

Yes, I didn't know before that "If a line is parallel to one side of a triangle and intersects the other two, then it divides them proportionally." So I took that into consideration, solved it and I got 108 :)

Answer 8

As it turned out, I used corresponding sides of similar triangles are in proportion.

What did you get for CF?

Answer 9

CF = DE because opposite sides of a parallelogram are congruent.

Answer 10

EF = 72
DE = 36

Answer 11

EF/AC = BC /BA
EF/90 = 120/150
EF = ?

Answer 12

I'll show you how I did it....

Answer 13

Okay.

Answer 14

BA = AC
BE = EF.
EF = BE*AC/BA
EF = 72.

BC = CA
BF = FE
BF = FE*BC/CA
BF = 144

Answer 15

I got 72 for EF.

Answer 16

That's correct.

Answer 17

And DE is equal to CF

Answer 18

DE + DF = 36 + 72 = 108.

You had 90.

Answer 19

At first I thought it was 90 for some reason, but after doing the math I also got 108 as my answer.

Answer 20

That sounds good. :) So, I guess we are finished with this problem.

Answer 21

Yes we are, thank you for everything @Directrix! :D

Answer 22

Alrighty, then. I'm happy to help. :)