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Medians in a triangle proof

  1. Jan 16, 2005 #1
    I know that the 3 medians of a triangle split the triangle into 6 similair triangles with equal area.

    I wish to know the proof for this using simple geometry.
     
  2. jcsd
  3. Jan 16, 2005 #2

    dextercioby

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    How do you know that??Did someone tell u,or you just invented it??

    Daniel.

    PS.If someone did tell u,why didn't u ask for the proof??Did u buy it,just like that??In mathematics,things don't work that way...
     
  4. Jan 16, 2005 #3
    let's say...
    you have a triangle ABC...
    D is the point in between A and B
    E is the point in between B and C
    F is the point in between C and A
    and O is the point 3 median lines intersect each other....

    AD=DB,AF=FC,BE=EC by definition
    area ADO=area BDO, area AFO=CFO, area BEO = CEO
    area ABE=ACE

    area ABO=ABE-BEO
    area ACO=ACE-CEO
    this implies ABO=ACO
    since ADO=DBO, ADO=1/2ABO
    since AFO=FCO, AFO= 1/2AFO=1/2ABO=ADO,
    so, AFO=FCO=ABO=ADO
    use the same method, you can show AFP=FCO=ABO=ADO=BEO=CEO
     
  5. Jan 16, 2005 #4

    dextercioby

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    So i think everything comes down to proving that the median of a side of a triangle divides the area enclosed by the triangle into 2 equisuperficial portions...

    Can u show that??

    BTW,the triangle does not have an area...

    Daniel.
     
  6. Jan 16, 2005 #5
    the base and the height of those two triangles have equal value
     
  7. Jan 16, 2005 #6

    dextercioby

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    Well,Vincentchan,i was obviously asking the OP... :grumpy:

    Daniel.

    PS.I knew you could answer it... :tongue2:
     
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