Varignon's theorem: Difference between revisions

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Re: the "proof without words", a suggested improvement to an already nice explanation (I won't protest a revert, or perhaps some of my changes will be kept but not others) to (a) use more consistent mathematical language once you get to the area variables (largely to make (b) easier) and (b) to tie things together a bit more clearly.
Tag: Reverted
Undid revision 1227982247 by Kevin Lamoreau (talk) my last edit didn't come out the way I meant it to
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|Bases of similar triangles are parallel to the blue diagonal.
|Ditto for the red diagonal.
|The base pairs form a parallelogram with half the area of the quadrilateral, ''A<sub>q</sub>'', as the sum of the areas of the four large triangles, ''A<sub>l</sub>'' is 2 ''A<sub>q</sub>'' (each of the two pairs reconstructs the quadrilateral) while that of the small triangles, ''A<sub>s</sub>'' is a quarter of ''A<sub>l</sub>''/4 (half linear dimensions yields quarter area) = ''A<sub>q</sub>''/2, and the area of the parallelogram is ''A<sub>q</sub>'' minus ''A<sub>s</sub>'' = ''A<sub>q</sub>'' − ''A<sub>q</sub>''/2 = ''A<sub>q</sub>''/2.
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