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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.
• Parallelogram: 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 and opposite angles are equal.
• Rectangle: each angle is a right angle. This implies that opposite sides are parallel and 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.

Quadrilateral is also the name of a group of fortresses in Italy.

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