Quadrilaterals include a square [A] with right-angles and all its sides equal and parallel; a rectangle [B] with only opposite sides equal; a trapezium [C] with only two opposite sides parallel; a rhombus [D] and a parallelogram [E], both with opposite sides parallel and no right-angles.

A quadrilateral is a polygon that has four sides and four vertices (corners). Quadrilaterals, and polygons in general, may be convex or concave. A convex quadrilateral may be further classified as a trapezoid or a British trapezium (one pair of opposite sides are parallel), a trapezium (no sides parallel); an isosceles trapezoid (U.S.) or an isosceles trapezium (U.K.) (two of the opposite sides parallel, the two other sides equal, and the two ends of each parallel side of equal angles); a parallelogram (opposite sides are parallel); a kite (two adjacent sides of equal length, the other two sides of equal length); a rhombus (four sides of equal length); a rectangle (each angle is a right angle); or a square (four sides of equal length, each angle a right angle). Quadrangular prisms and quadrangular pyramids are ones whose bases are quadrilateral.


Ptolemy's theorem

Ptolemy's theorem states that the sum of the products of the two pairs of opposite sides of a convex cyclic quadrilateral is equal to the product of the lengths of the diagonals. It is named after the mathematician, astronomer, and geographer Ptolemy of Alexandria.