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Vector Proofs: A Quadrilateral thing #2!

  1. Nov 10, 2005 #1
    I'm not sure if I should've started a new thread for this but..

    I need some help trying to prove that the diagonals of a parallelogram bisect each other..
    I think I have an idea of how to solve this but I can't seem to put it together:

    Given
    AB = DC
    AD = BC

    Known
    AB + BC = AC
    BC + BD = BD
    and so forth..

    I'm trying to prove that BZ = ZD and AZ = ZC. Using position vectors, I determined that the midpoint of vector AC to be OA + OB/2 = OZ and that AZ = OA - OZ and ZC = OZ - OC. I had the train of thought in my mind on how to persue this problem before but I lost it somehow after thinking too hard. I know these are the right steps that need to be considered to finish the problem, but in what steps do I need to do in order to finish this problem?

    [​IMG]
     
    Last edited: Nov 10, 2005
  2. jcsd
  3. Nov 10, 2005 #2

    lightgrav

    User Avatar
    Homework Helper

    where's the middle of a vector?
     
  4. Nov 10, 2005 #3
    its a midpoint. Hence OA + OB/2 = OZ.

    So far, my steps are:

    1 - AZ = OA - OZ
    2 - ZC = OZ - OC

    sub into 1 -> AZ = OA - (OA + OB/2)
    sub into 2 -> ZC = (OA + OB/2) - OC

    but after this, I get lost in trying to prove how AZ = ZC.
     
    Last edited: Nov 10, 2005
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