Question

In Triangle ABC shown below, side AB is 6 and side AC is 4.



Which statement is needed to prove that segment DE is parallel to segment BC and half its length?
Answer
Segment AD is 3 and segment AE is 2.
Segment AD is 3 and segment AE is 4.
Segment AD is 12 and segment AE is 4.
Segment AD is 12 and segment AE is 8.

Answer 1

The first one.

Answer 2

explain sir :P?

Answer 3

Do you know what similar triangles are?

Answer 4

I believe so, yea

Answer 5

So, if DE and BC are parallel, triangles ADE and ABC have to be similar. This means the ratio of AB/AC has to equal AD/AE.

Now, what's the ratio of AB/AC?

Answer 6

um idk

Answer 7

You have the lengths of AB and AC, don't you?

Answer 8

It's given, you have it in your question.

Answer 9

oh, 3/2?

Answer 10

Yes, so this means AD/AE should also equal 3/2. From the four options, which ones have ratio 3/2?