Quadrilaterals
Quadrilaterals include the square, rectangle, trapezium, trapezoid, rhombus, kite and parallelogram. Quadrilaterals can be concave, convex, cyclic, tangential, extangential, orthodiagonal, equidiagonal or bicentric. Most of these properties are obscure, but a similarly exhaustive list of triangle properties would fill many pages. When in doubt on a quadrilateral, add a diagonal to make two triangles.