Crossed rectangle
| Rectangle | |
|---|---|
Rectangle
|
|
| Type | quadrilateral, parallelogram, orthotope |
| Edges and vertices | 4 |
| Schläfli symbol | { } × { } |
| Coxeter diagram |   |
| Symmetry group | Dihedral (D2), [2], (*22), order 4 |
| Dual polygon | rhombus |
| Properties | convex, isogonal, cyclic Opposite angles and sides are congruent |
In Euclidean plane geometry, a rectangle is a quadrilateral with four right angles. It can also be defined as an equiangular quadrilateral, since equiangular means that all of its angles are equal (360°/4 = 90°). It can also be defined as a parallelogram containing a right angle. A rectangle with four sides of equal length is a square. The term is occasionally used to refer to a non-square rectangle. A rectangle with vertices ABCD would be denoted as 
ABCD.
The word rectangle comes from the Latin rectangulus, which is a combination of rectus (right) and angulus (angle).
A crossed rectangle is a crossed (self-intersecting) quadrilateral which consists of two opposite sides of a rectangle along with the two diagonals. It is a special case of an antiparallelogram, and its angles are not right angles. Other geometries, such as spherical, elliptic, and hyperbolic, have so-called rectangles with opposite sides equal in length and equal angles that are not right angles.
Rectangles are involved in many tiling problems, such as tiling the plane by rectangles or tiling a rectangle by polygons.
A convex quadrilateral is a rectangle if and only if it is any one of the following:
A rectangle is a special case of a parallelogram in which each pair of adjacent sides is perpendicular.
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Wikipedia