Not sure about these ratios.

Question

anonymous · Answer

attachment

anonymous · Answer

|dw:1362519837571:dw|

anonymous · Answer

Is that right?

experimentx · Answer

yes yes ... they are parallel ... but your reason is not correct.

experimentx · Answer

you have to show it.

experimentx · Answer

hmm ... show that those two triangles are similar.

mathstudent55 · Answer

What do you know about two triangles in which two sides of one triangle are proportional to two sides of the the other triangle and the included angles are congruent.

anonymous · Answer

I don't know how to show that they are similar.....I know that AM and AN are both 1/3 of AB and AC respectively.

anonymous · Answer

Oh so.....that triangle has to be isosceles so it will have the same angles as ABC

mathstudent55 · Answer

Do you know how to prove that triangles are congruent? If you do, which methods do you know?

mathstudent55 · Answer

Hint: the methods of proving triangles congruent are known for initials, usually A's and S's in groups of three.

anonymous · Answer

I know all three of them but how are those going to help me?

mathstudent55 · Answer

The triangles are not necessarily isosceles.

mathstudent55 · Answer

Can you list them?

anonymous · Answer

ASA....SAS....AAA

mathstudent55 · Answer

We're getting there very soon.

anonymous · Answer

So I should probably use SAS

mathstudent55 · Answer

Not, AAA.
ASA, SAS, AAS, SSS

anonymous · Answer

That's what I meant....sorry

anonymous · Answer

But still....SAS

mathstudent55 · Answer

These are methods of proving triangles cvongruent.
For example SAS for congruence is:
If two sides of a triangle are congruent to two sides of another triangle, and the included angles are congruent, the triangles are congruent.

mathstudent55 · Answer

There is SAS for similarity, but it goes like this:

mathstudent55 · Answer

SAS Similarity:
If the lengths of two sides of a triangle are proportional to the lengths of two sides of another triangle, and the included angles are congruent, then the triangles are similar.

mathstudent55 · Answer

In this problem you are given AM : AB = AN : AC. When two ratios are equal, that creates a proportion. That shows that the lengths of two sides of triangle ANM are proportional to the lengths of two sides of triangle ACB. Also, the included angle A of triangle ANM is congruent to the included angle A of triangle ACB.
You have exactly what you need for SAS Similarity, so you can say triangle ACB is similar to triangle ANM.

mathstudent55 · Answer

Once you have proven the triangles are similar, you can easily prove the segments are parallel.