In geometry, a quadrilateral is a polygon with four sides and four vertices. Quadrilaterals, and polygons in general, are broadly divided into two groups: convex and concave polygons. Convex quadrilaterals are further classified as follows:
- Trapezoid or trapezium (Brit. Eng): one pair of opposite sides are parallel.
- Trapezium (Amer. Eng.): no sides are parallel.
- Isosceles trapezium (Brit. Eng.) or isosceles trapezoid (Amer. Eng.): two of the opposite sides are parallel, the two other sides are equal, and the two ends of each parallel side have equal angles. This implies that the diagonals have equal length.
- Parallelogram: both pairs of opposite sides are parallel. This implies that opposite sides have equal length, and that opposite angles are equal.
- Kite: two adjacent sides have equal length, the other two sides have equal length. This implies that one set of opposite angles is equal, and that diagonals are perpendicular.
- Rhombus: four sides have equal length. This implies that opposite sides are parallel, opposite angles are equal, and the diagonals are perpendicular.
- Rectangle: each angle is a right angle. This implies that opposite sides are parallel and have equal length, and the diagonals have equal length.
- Square (regular quadrilateral): four sides have equal length, and each angle is a right angle. This implies that opposite sides are parallel, and the diagonals are both perpendicular and equal length.
Quadrilateral is also the name of a group of fortresses in Italy and of the southern part of Dobrudja, ceded by Romania to Bulgaria in the opening month of World War II (see Romania during World War II).
