Question

Help me please
1. In ABC, centroid D is on median . AD = x + 5 and DM = 2x – 1. Find AM.
Picture on bottom
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7. If mDBC = 65º, what is the relationship between AD and CD? The diagram is not to scale.

Answer 1

number 1

Answer 2

number 7

Answer 3

For #1, are you supposed to solve for x? If so, I don't think there is enough information...

Answer 4

Nevermind. Ok, teacher mode: What do you know about the "midline theorem"?

Answer 5

Nothing i think i should look it up though

Answer 6

Yup. There is a proof that I will go through to help you solve your problem, for a numerical answer. In short, the midline theorem says "the segment connecting the midpoints of two sides of a triangle is parallel to, and half the length of, the third side. let me know if you understand that.

Answer 7

You remember what a centroid is?

Answer 8

Centroid of a triangle is the point of intersection of all its three medians.
The centre of mass of a uniform object is also called as Centroid.

Answer 9

Textbook answer. Perfect. Ok, so now we have everything we need. we want to find "x". So we're going to look for the relationship between AD and DM, in other words, what is AD/DM?

Answer 10

It might help to draw and extended line through D and C

Answer 11

D is the middle of A and M so AD/DM and are the line the i need to add and find the A/M of the segment

Answer 12

I thought D was the centroid? :DDD

Answer 13

yeah

Answer 14

sorry im horribble at geomntry

Answer 15

No worries. I am too. It's a very difficult subject.

Answer 16

Ok, for some reason the draw tool isn't working for me. So I'll do this the hard way.

Hopefully, you can see a triangle ADC. What would happen if you took the midpoints of AD and DC, and drew a line segment though them? What would be special about that segment?

Answer 17

hmmm special about the sement!!!! uhmm the equations

Answer 18

Just to be clear. Taking the original post:

1. extend a segment through C and D. Hits AB at, say, P.
2. Connect P and M. How does this line relate to AC?
2. Take the midpoints of AD and DC, Q and R respectively. Connect them. How does THIS segment relate to AC?

Think about the midline theorem.

Answer 19

Draw it out exactly. Don't worry, we ARE making progress, just trust me.

Answer 20

Remember the midline theorem, "parallel and 1/2 the length".

Answer 21

For the segment AM in triangle ABC, when the centroid D is on median segment AM and AD=x+5 and DM=2x-1, when you solve for x, then x is equal to 7/3. So 7/3 + 5 = 22/3. And, 2(7/3)-1 = 11/3. The solution 11/3 + 22/3 = 11

Answer 22

How do you solve for x?

Answer 23

a useful property of the centroid is that it is two thirds of the way down the median from the vertex. This means that AD=2DM.

Answer 24

That is also the theorem I was using. I was going through the proof of the theorem. We're almost to the end, but it's aubreyk9614's call if I should keep going.

Answer 25

i am sorry i didn't read the whole convo.

Answer 26

No problem I have a tendency to be long-winded. But I think it helps for geometry to really have to think about the steps involved - all of them - to arrive at a solution. It's more useful to be able to know many things from few things, than to simply memorize many things. more rewarding too, IMO.

Answer 27

Aaaaaaaaaand he's gone. Oh well. I tried.

Answer 28

long story short, PMQR define a //ogram. diags of //ogram bisect eachother. proof follows from there.

Answer 29

well i am not good at proofs really.