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Mathematics
OpenStudy (anonymous):

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.

OpenStudy (anonymous):

OpenStudy (anonymous):

The first one.

OpenStudy (anonymous):

explain sir :P?

OpenStudy (anonymous):

Do you know what similar triangles are?

OpenStudy (anonymous):

I believe so, yea

OpenStudy (anonymous):

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?

OpenStudy (anonymous):

um idk

OpenStudy (anonymous):

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

OpenStudy (anonymous):

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

OpenStudy (anonymous):

oh, 3/2?

OpenStudy (anonymous):

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

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