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#1 2008-12-09 20:26:03
- Identity
- Member
- Registered: 2007-04-18
- Posts: 934
Vector proof
Ok, so this came about when I tried to prove:
"If the midpoints of the sides of a rectangle are joined, a rhombus is formed."
Long story short, I tried to prove that the rhombus WXYZ (formed from rectangle OABC), has equal side lengths and that led me to this hypothesis:
If
, thenCan someone please help me with this or provide a counterproof?
Last edited by Identity (2008-12-09 20:26:39)
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#2 2008-12-09 23:08:01
- Kurre
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- Registered: 2006-07-18
- Posts: 280
Re: Vector proof
The left hand side (after squaring) is equal to a^2+2ac+c^2=a^2+c^2, and the right hand side is equal to a^2-2ac+c^2=a^2+c^2. so yes, it holds.
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#3 2008-12-09 23:20:49
- Identity
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- Registered: 2007-04-18
- Posts: 934
Re: Vector proof
Ah, thanks Kurre, so
Didn't see how it would follow through at first, but then realised
Nice!
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