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===Special cases===
The Varignon parallelogram is a [[rhombus]] if and only if the two diagonals of the quadrilateral have equal length, that is, if the quadrilateral is an [[equidiagonal quadrilateral]].<ref name=deV>{{citation
| last = de Villiers | first = Michael
| isbn = 9780557102952
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| year = 2009}}.</ref>
The Varignon parallelogram is a [[rectangle]] if and only if the diagonals of the quadrilateral are [[perpendicular]], that is, if the quadrilateral is an [[orthodiagonal quadrilateral]].<ref name=Josefsson/>{{rp|p. 14}} <ref name=deV />{{rp|p. 169}}
If a crossing quadrilateral is formed from either pair of opposite parallel sides and the diagonals of a parallelogram, the Varignon parallelogram is a line segment traversed twice.
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