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.

The figure shows triangle ABC with segments DE and EF. Point D is on side AB, point E is on side AC and point F is on side BC. Segment AD is 6, segment AE is 12, segment EC is 18, and segment FC is 24

Which statement can be proved true using the given theorem?

Segment BD = 12

Segment BD = 4

Segment BF = 16

Segment BF = 9

Answer 1

My guess was 16. am I right?

Answer 2

@ash2326 Can you tell me if im right or wrong?

Answer 3

yes, how did you find that?

Answer 4

I assumed it all had to be equal..like I said it was really a guess, so 16 is right? Could you show me how I get that?

Answer 5

yes,

Answer 6

When a line parallel to a side is drawn in a triangle, it divides the other two sides in the same ratio.
Suppose in triangle ABC, DE is the line parallel to BC
Do you follow this?

Answer 7

Yes (:

Answer 8

So there are two results that follow this
\[\frac{AD}{AB}=\frac{AE}{AC}\]
\[\frac{AD}{DB}=\frac{AE}{EC}\]
For this question, second one is useful

Answer 9

This is the theorem given in the question
"Theorem: A line parallel to one side of a triangle divides the other two proportionately."
So we just wrote the relations we get

Answer 10

*from this theorem

Answer 11

Do you follow?

Answer 12

Okay I think I understand this now (: THank you very much

Answer 13

Really?

Answer 14

I just needed to re jog my memory

Answer 15

cool :)