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Question
The diagonals of parallelogram bisect eachother.Prove by vector method
Here is one way:
Let the intersection pt O of the diagonals be the origin,then
a,b,c,d are the position vectors of the vertices A,B,C,D.
For parallelogram, a-b=d-c ==> a+c=b+d ==> |a+c|=|b+d|
For a common parallelogram,the last result does not hold unless
a+c=0 and b+d=0, that is a=-c and b=-d ==> |a|=|c| and |b|=|d|.
Another way can be seen here:
http://farside.ph.utexas.edu/teaching/301/lectures/node30.html
Abe
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Calculus
Answers by Expert:
Abe Mantell
Expertise
Hello, I am a college professor of mathematics and regularly teach all levels from elementary mathematics through differential equations, and would be happy to assist anyone with such questions!
Experience
Over 15 years teaching at the college level.
Organizations
NCTM, NYSMATYC, AMATYC, MAA, NYSUT, AFT.
Education/Credentials
B.S. in Mathematics from Rensselaer Polytechnic Institute
M.S. (and A.B.D.) in Applied Mathematics from SUNY @ Stony Brook
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