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March 12, 2026, 12:47:35 pm

Author Topic: Pretty simple Vector Proof  (Read 847 times)  Share 

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BlueYoHo

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Pretty simple Vector Proof
« on: February 17, 2009, 06:24:16 pm »
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Ok i have this Question that i don't really know how to go any further. The question says:
Prove that if the midpoints of the sides of a quadrilateral are joined then a parallelogram is formed.

Ok so I've got my shape with 4 sides, lol, and i've labeled the corners: O (bottom-left), A (top-left), B (top-right), C (bottom-right).
OA=a
OB=b                                                                               b
CB=c                                                                A_________X.__________B
CO=d                                                                 |                               |
                                                                        |                               |
                                                                a    W|                               |Y  c
                                                                        |                               |
                                                                        |                               |
                                                                     O |             Z.               |C
                                                                                       d
                                                                       
It's probably the worst diagram in VN history but anyway...
I know I'm supposed to prove that the opposite sides are parallel
and am i also supposed to prove that the opposite sides have the same magnitude?


So far I've got:
WX= 1/2 (a+b)
ZY= 1/2 (c-d)
and i don't know how to prove that they're parallel.



yeah... any help would be appreciated.
2009 - VCE Enter: 96.05
2010 - Monash University: BCom/BMechatronicEng

Mao

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Re: Pretty simple Vector Proof
« Reply #1 on: February 17, 2009, 08:09:20 pm »
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you have to prove one pair of sides are parallel and of equal magnitude.
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