squares be drawn on all sides of a quadrilateral. The segments connecting the centers of opposite squares are (a) equal in length, and (b) perpendicular. Thus these centers are the vertices of an orthodiagonal quadrilateral. This is called Van Aubel's theorem. For any simple quadrilateral with given edge lengths, there is a cyclic quadrilateral with the same edge lengths. The four smaller triangles formed by the diagonals and sides of a convex quadrilateral have the property that the product of the areas of two opposite triangles equals the product of the areas of the other two triangles. Taxonomy A hierarchical taxonomy of quadrilaterals is illustrated by the figure to the right. Lower classes are special cases of higher classes they are connected to. Note that "trapezoid" here is referring to the North American definition (the British equivalent is a trapezium). Inclusive definitions are used throughout. Skew quadrilaterals A non-planar quadrilateral is called a skew quadrilateral. Formulas to compute its dihedral angles from the edge lengths and the angle between two adjacent edges were derived for work on the properties of molecules such as cyclobutane that contain a "puckered" ring of four atoms. Historically the term gauche quadrilateral was also used to mean a skew quadrilateral. A skew quadrilateral together with its diagonals form a (possibly non-regular) tetrahedron, and conversely every skew quadrilateral comes from a tetrahedron where a pair of opposite edges is removed. See also Complete quadrangle Perpendicular bisector construction of a quadrilateral Saccheri quadrilateral Quadrangle (geography) References External links Quadrilaterals Formed by Perpendicular Bisectors, Projective Collinearity and Interactive Classification of Quadrilaterals from cut-the-knot Definitions and examples of quadrilaterals and Definition and properties of tetragons from Mathopenref A (dynamic) Hierarchical Quadrilateral Tree at Dynamic Geometry Sketches An extended classification of quadrilaterals at Dynamic Math Learning Homepage The role and function of a hierarchical classification of quadrilaterals by Michael de Villiers 4 (number)