#Why is the center of a parallelogram the point of intersection of it's diagonals?

14 messages · Page 1 of 1 (latest)

safe sand
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Is there a proof without involving coordonates? Would be better if it would involve vectors and linear/affine combination of them.
Also what is the significance of the center of a triangle with coordonates a/3 + b/3 + c/3, where a,b,c are the coordonate points of the vertices of the triangle in the xOy cartesian system?
What about 4 points, a,b,c,d and the point defined as (a+b+c+d)/4, what does it mean?

acoustic flintBOT
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fluid egret
safe sand
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Bruh

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Why is it a definition

fluid egret
safe sand
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Like why is the center of a parallelogram the intersection of it's diagonals

fluid egret
safe sand
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Idk

fluid egret
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Then how can you possibly prove anything about something that isn't defined?

safe sand
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Ok then

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Why is the point of intersection of a parallelogram half way for both diagonals?

last sage