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Vector Proofs: A Quadrilateral thing!

  1. Nov 10, 2005 #1
    Vector Proofs: A Quadrilateral thing #2!

    Thanks lightgrav!
     
    Last edited: Nov 10, 2005
  2. jcsd
  3. Nov 10, 2005 #2
    re:

    We had that problem on a geometry test in 9th grade, I will try digging it up and show you how :smile: ...if I can find it of course :rolleyes:
     
  4. Nov 10, 2005 #3
    Any help is always appreciated!
     
  5. Nov 10, 2005 #4

    lightgrav

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    you're given that dz = zb and az = zc , as your starting point.

    What sums and differences of these equations show what you want?
     
  6. Nov 10, 2005 #5
    az + zb = ab
    cz + zd = cd

    but az = zb, cz = cd therefore ab = cd!

    Bah! That took like 5 minutes to see when I was spending 5 hours worth of time on it.

    Thanks!
     
  7. Nov 10, 2005 #6

    lightgrav

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    The key to this stuff is writing in symbols
    JUST WHAT they tell you in words.

    That's why everybody calls these things "Word Problems"!
     
  8. Nov 10, 2005 #7
    But a new problem arises :\.
     
  9. Nov 10, 2005 #8

    Diane_

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    One way to do this is to show that you have a pair of congruent triangles. (There are actually several pair, but you only need one.) Remember the definition of a parallelogram - that'll give you the angles. There's one more property of parallelograms that will give you the sides that you need.
     
  10. Nov 10, 2005 #9
    I need to do this through vector proofs, though. If I could use congruent triangles, I would've been long done this problem :).
     
  11. Nov 11, 2005 #10

    daniel_i_l

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    You just have to show that 1/2(dc+da) = 1/2db. that means that the middle of db touches the middle of ac. This is easy to prove. Start with the two equations:
    db = da + ab
    db = dc + cb
    and try to solve for 1/2(dc+da) in terms of db.
     
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