In Euclidean plane geometry, a rectangle is a rectilinear convex polygon or a quadrilateral with four right angles.

The word rectangle comes from the Latin rectangulus, which is a combination of rectus (as an adjective, right, proper) and angulus (angle).

A parallelogram is a special case of a trapezium (known as a trapezoid in North America) in which both pairs of opposite sides are parallel and equal in length.

A trapezium is a convex quadrilateral which has at least one pair of parallel opposite sides.

Quadrilaterals with two axes of symmetry, each through a pair of opposite sides, belong to the larger class of quadrilaterals with at least one axis of symmetry through a pair of opposite sides.

A rectangle is cyclic: all corners lie on a single circle.

It is isogonal or vertex-transitive: all corners lie within the same symmetry orbit.

The dual polygon of a rectangle is a rhombus, as shown in the table below.

[10] A rectangle is a rectilinear polygon: its sides meet at right angles.

A rectangle in the plane can be defined by five independent degrees of freedom consisting, for example, of three for position (comprising two of translation and one of rotation), one for shape (aspect ratio), and one for overall size (area).

The midpoints of the sides of any quadrilateral with perpendicular diagonals form a rectangle.

The Japanese theorem for cyclic quadrilaterals[12] states that the incentres of the four triangles determined by the vertices of a cyclic quadrilateral taken three at a time form a rectangle.

The British flag theorem states that with vertices denoted A, B, C, and D, for any point P on the same plane of a rectangle:[13] For every convex body C in the plane, we can inscribe a rectangle r in C such that a homothetic copy R of r is circumscribed about C and the positive homothety ratio is at most 2 and

A crossed quadrilateral is sometimes likened to a bow tie or butterfly, sometimes called an "angular eight".

A three-dimensional rectangular wire frame that is twisted can take the shape of a bow tie.

The interior of a crossed rectangle can have a polygon density of ±1 in each triangle, dependent upon the winding orientation as clockwise or counterclockwise.

A crossed rectangle may be considered equiangular if right and left turns are allowed.

The lowest number of squares need for a perfect tiling of a rectangle is 9[19] and the lowest number needed for a perfect tilling a square is 21, found in 1978 by computer search.

[20] A rectangle has commensurable sides if and only if it is tileable by a finite number of unequal squares.