A quadrilateral, in the mathematical area of geometry, is a closed figure formed by four line segments. It can also be defined as a polygon (many-sided geometric figure) with four straight sides and four vertices (points on a geometrical figure). The word quadrilateral comes from the Latin word quadrilaterus, meaning four-sided.
Geometrically, it can be defined as four points, such as W, X, Y, and Z, that all are contained in the same plane, where no three of the points are in the same line (collinear). Thus, when the four segments, WX, XY, YZ, and ZW, intersect only at their end-points the resulting union is called a quadrilateral. Special cases of a quadrilateral are: (1) A trapezium—A quadrilateral with no pairs of opposite sides parallel (Figure A). (2) A trapezoid—A quadrilateral with one pair of sides parallel (Figure B). (3) A parallelogram—A quadrilateral with two pairs of sides parallel (Figure C). (4) A rectangle—A parallelogram with all angles right angles (Figure D). (5) A square—A rectangle having all sides of the same length (Figure E). A complete quadrilateral is a plane figure in projective geometry consisting of lines a, b, c, and d (no two of them concurrent) and their points of intersection (Figure F).
Other cases of quadrilaterals are: isosceles trapezoid (where two of the opposite sides are parallel and the remaining two sides are equal; while the two ends of the two parallel sides have equal angles); rhombus (where its four sides have sides of equal length and two axes of symmetry); rhomboid (where the adjacent
sides have unequal lengths and the angles are not right angles [oblique]); and kite (where two adjacent sides have equal lengths, and the other two sides also have equal lengths).
See also Polygons.