## Definitions and some Properties of Quadrilaterals

The quadrilaterals below are listed in order from top to bottom, and from left to right in correspondence with the dynamic Hierarchical Quadrilateral Tree where this page is linked from, but the duals of each other are grouped together next to each other to display the side-angle duality. Only a selection of some important properties are given. Since quadrilaterals lower down in the hierarchy inherit ALL the properties from those they are linked to from above, only some additional properties are given lower down. Also note that each of the quadrilaterals below can be mathematically defined in several different, but equivalent ways. So the definitions below, mostly based on symmetry, are not unique.

Quadrilateral - Closed, plane figure with four vertices A, B, C and D, connected by four straight sides AB, BC, CD and DA. Properties: If convex, no reflexive angles, both diagonals interior & interior angle sum is 3600. If concave, one reflexive angle, one diagonal exterior & interior angle sum is 3600. If crossed, two reflexive angles, two diagonals exterior & interior angle sum is 7200.