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Adding short description: "The midpoints of the sides of an arbitrary quadrilateral form a parallelogram" (Shortdesc helper) |
→Proof: Add Proof without words |
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[[Image:Varignon parallelogram crossed.svg|300px]]
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[[File:varignon_parallelogram.svg|thumb|[[Proof without words]] of Varignon's theorem:
<br />1. An arbitrary quadrilateral and its diagonals.
<br />2. Bases of similar triangles are parallel to the blue diagonal.
<br />3. Ditto for the red diagonal.
<br />4. 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>'' (half linear dimensions yields quarter area), and the area of the parallelogram is ''A<sub>q</sub>'' minus ''A<sub>s</sub>''.]]
==The Varignon parallelogram==
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