Understanding Triangle Medians and Their Proportions

[momentum]

i have heard

when you draw a median in a triangle ...the median gets 2:1 bisected


i want to know when this happens ?

which one is the bigger portion ?

which one is the lower portion ?

can you please tell me the details of it.

can u please provide me a specific web page which explains this stuff ?


thank you

 

[dextercioby]

I simply can't figure out what you mean. Can you post a drawing of that triangle...?

Daniel.

 

[momentum]

nobody replied.

if medians sects each other who is "2" and who is "1" ...so i want to know about 2:1 formula.

which situation this rule works ?

can you please provide me a tutorial for this ?

 

[momentum]

here i have uploaded the image

http://img69.imageshack.us/my.php?image=math7of.jpg

in which situation that works ?

does AO:OD=2:1

OR

AO:OD=1:2


which one is correct ?

 

[VietDao29]

here i have uploaded the image

http://img69.imageshack.us/my.php?image=math7of.jpg

in which situation that works ?

does AO:OD=2:1

OR

AO:OD=1:2


which one is correct ?

What do you mean? I don't really get that?
What does the problem actually say?
Which one is the median, and which one is the bisector?
Or do you mean the centroid of a triangle (i.e, the single point where the 3 medians in a triangle intersect each other)? :)

 

[Mathyards]

OD = 1/3 AD ; AO = 2/3 AD

AO = 2OD ; AO:OD = 2 : 1

or OD : AO = 1 : 2

 

[momentum]

What do you mean? I don't really get that?
do you mean the centroid of a triangle (i.e, the single point where the 3 medians in a triangle intersect each other)? :)

yes...probabily you are right.

in fact i don't know the details.

all i know is , a median is divided into 2:1 ratio sometimes ...but when ? i don't know. ...thats what i want to know.

can you please tell when does it occur ?

does it occur when 3 medians intersects each other ?

well, suppose 3 medians intersect each other, so that means each of the median is divided into 2:1 ratio ...but which portion is 2 and which portion is 1 ?

does the
top-->center=2
and
center-->bottom(middle of a side)=1


is this correct ?


Please provide me a tutorial.
i want to know about this thing.

i could not search "google" becuase i don't know what search keywords i should use to search .


thank you

 

[VietDao29]

yes...probabily you are right.

in fact i don't know the details.

all i know is , a median is divided into 2:1 ratio sometimes ...but when ? i don't know. ...thats what i want to know.

can you please tell when does it occur ?

does it occur when 3 medians intersects each other ?

well, suppose 3 medians intersect each other, so that means each of the median is divided into 2:1 ratio ...but which portion is 2 and which portion is 1 ?

does the
top-->center=2
and
center-->bottom(middle of a side)=1


is this correct ?


Please provide me a tutorial.
i want to know about this thing.

i could not search "google" becuase i don't know what search keywords i should use to search .


thank you

In the post #5, I did provide you the link to a wikipedia article about triangle. In the article, you will fnd a part that tells you something about the centroid. It's in the Points, lines and circles associated with a triangle section (number 3).
--------------
I'll give you a brief explanation if you want. But I may say, my terminology is not the best.
Let ABC be a triangle, and AM be one of its median. $$M \in BC$$
We define the point G on the line segment AM such that:
$$\frac{AG}{GM} = \frac{2}{1} \quad \mbox{or} \quad \frac{AG}{AM} = \frac{2}{3} \quad \mbox{or} \quad \frac{MG}{AM} = \frac{1}{3}$$.
Then G is the centroid of the triangle ABC.
That is, the median BN, and CK pass through G.
And if we have 3 medians AM, BN, CK, they will intersect each other at only one point, namely G (the centroid).
Can you get it? :)

 

[geniusprahar_21]

the centroid of a triangle has many 2:1 properties.

consider triangle ABC, with medians AD, BE, and CF.

1. Centroid G divides medians in the ratio 2:1, so that $$\frac{AG}{GD} = \frac{BG}{GE} = \frac{CG}{GF} = \frac {2}{1}$$

2. the centroid G divides the line joining the circumcentre O and the orthocentre H in the ratio 2:1 so that $$\frac{HG}{CG} = \frac{2}{1}$$

3. the foot of the perpendiculars P, Q, and R from the centroid to altitudes, divides the altitudes AX, BY, and CZ in the ratio 2:1. that is $$\frac{AP}{PX} = \frac{BQ}{QY} = \frac{CR}{RZ} = \frac{2}{1}$$

i am sure there are more such properties of the centroid, (though its a guess)... the moment i find out more, i'll post it...

 

[momentum]

Hi, centroid is a complex thing.

can i ask 2 questions on this centroid ?


does all triangle have centroid ? does all triangles medians intesect each other in a common point which is called the centroid ?


OR ,


there are few triangles (who are they ?) which has centroid ?


please answer.

thanks

 

[VietDao29]

Hi, centroid is a complex thing.

can i ask 2 questions on this centroid ?


does all triangle have centroid ? does all triangles medians intesect each other in a common point which is called the centroid ?


OR ,


there are few triangles (who are they ?) which has centroid ?


please answer.

thanks

Every triangle has a centroid, the centroid is defined to bo the intersection of its 3 medians.
There should be a proof of 3 medians in a triangle intersect each other at only 1 point in your textbook, and that point is called the centroid of that triangle.
Can you get this? :)

 

[momentum]

beautiful....thanks