Quadrilateral
In Euclidean plane geometry, a quadrilateral is a polygon with four edges (or sides) and four vertices (or corners). Sometimes, a quadrilateral is called a quadrangle (similar to the term "triangle"), while other times, the term tetragon is used (similar to other polygon names such as pentagon and hexagon). The origin of the word quadrilateral is the two Latin words quadri, a variant of four, and latus, meaning "side".
| Quadrilateral | |
|---|---|
 Some types of quadrilaterals | |
| Edges and vertices | 4 |
| Schläfli symbol | {4} (for square) |
| Area | various methods, usually base time height |
| Internal angle (degrees) | 90° (for square and rectangle) |
A quadrilateral with vertices [math]\displaystyle{ A }[/math], [math]\displaystyle{ B }[/math], [math]\displaystyle{ C }[/math], [math]\displaystyle{ D }[/math] is sometimes written as [math]\displaystyle{ \square ABCD }[/math].[1][2][3]
All the sides of a quadrilateral are straight, and the interior angles of a quadrilateral add up to 360°.[3]
- [math]\displaystyle{ \angle A+\angle B+\angle C+\angle D=360^{\circ}. }[/math]
This is a special case of the n-gon interior angle sum formula: (n − 2) × 180°.
Almost all quadrilaterals tile the plane, by repeated rotation around the midpoints of their edges. The only quadrilaterals that do not do this are the ones with edges that intersect with each other.
Kinds of quadrilaterals
Quadrilaterals can be either complex, also called crossed (self-intersecting), or simple (not self-intersecting). Simple quadrilaterals are either convex or concave.
There are different kinds of simple quadrilaterals. A trapezoid is a quadrilateral with one pair of parallel edges, where one edge is shorter than the other. A parallelogram is a quadrilateral with two pairs of parallel edges.
Squares, rectangles, and rhombuses are special types of parallelograms.[3] A rectangle has four right angles, while a rhombus has four sides of the same length. A square has four right angles and four sides of the same length, making it a regular polygon. This makes squares a type of rectangle and rhombus.
Quadrilateral Media
Euler diagram of some types of simple quadrilaterals. (UK) denotes British English and (US) denotes American English.
Convex quadrilaterals by symmetry, represented with a Hasse diagram
Great rhombihexacron facets
The Varignon* parallelogram EFGH
A taxonomy of quadrilaterals, using a Hasse diagram
The (red) side edges of tetragonal disphenoid represent a regular zig-zag skew quadrilateral.
Related pages
References
- ↑ "List of Geometry and Trigonometry Symbols". Math Vault. 2020-04-17. Retrieved 2020-09-01.
- ↑ Weisstein, Eric W. "Quadrilateral". mathworld.wolfram.com. Retrieved 2020-09-01.
- ↑ 3.0 3.1 3.2 "Quadrilaterals - Square, Rectangle, Rhombus, Trapezoid, Parallelogram". www.mathsisfun.com. Retrieved 2020-09-01.