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2:1 formula

  1. Mar 29, 2006 #1
    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
     
  2. jcsd
  3. Mar 30, 2006 #2

    dextercioby

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

    Daniel.
     
  4. Mar 30, 2006 #3
    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 ?
     
  5. Mar 30, 2006 #4
  6. Mar 30, 2006 #5

    VietDao29

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    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)? :)
     
  7. Mar 30, 2006 #6
    OD = 1/3 AD ; AO = 2/3 AD

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

    or OD : AO = 1 : 2
     
  8. Mar 31, 2006 #7
    yes...probabily you are right.

    in fact i dont know the details.

    all i know is , a median is divided into 2:1 ratio sometimes .....but when ? i dont 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 dont know what search keywords i should use to search .


    thank you
     
  9. Mar 31, 2006 #8

    VietDao29

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    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. [tex]M \in BC[/tex]
    We define the point G on the line segment AM such that:
    [tex]\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}[/tex].
    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? :)
     
  10. Apr 2, 2006 #9
    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 [tex]\frac{AG}{GD} = \frac{BG}{GE} = \frac{CG}{GF} = \frac {2}{1} [/tex]

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

    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 [tex] \frac{AP}{PX} = \frac{BQ}{QY} = \frac{CR}{RZ} = \frac{2}{1} [/tex]

    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....
     
  11. Apr 4, 2006 #10
    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
     
  12. Apr 5, 2006 #11

    VietDao29

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    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 text book, and that point is called the centroid of that triangle.
    Can you get this? :)
     
  13. Apr 5, 2006 #12
    beautiful.............thanks
     
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