Varignon's theorem: Difference between revisions

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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: {{olist

<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_q'', as the sum of the areas of the four large triangles, ''A_l'' is 2 ''A_q'' (each of the two pairs reconstructs the quadrilateral) while that of the small triangles, ''A_s'' is a quarter of ''A_l'' (half linear dimensions yields quarter area), and the area of the parallelogram is ''A_q'' minus ''A_s''.]]

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==The Varignon parallelogram==