Quadrilateral
In Euclidean plane geometry, a quadrilateral is a polygon with four edges (or sides) and four vertices (or corners). Sometimes, the term quadrangle is used (similar to the term "triangle"), while other times, the term tetragon is used (similar to pentagon, 5-sided polygon, and hexagon, 6-sided polygon). 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]
| 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) |
The origin of the word quadrilateral is the two Latin words quadri, a variant of four, and latus, meaning "side".
Quadrilaterals can be either complex, also called crossed (self-intersecting), or simple (not self-intersecting). Simple quadrilaterals are either convex or concave.
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°.
All non-self-crossing quadrilaterals tile the plane, by repeated rotation around the midpoints of their edges.
There are 6 special kinds of quadrilaterals; square, rectangle, rhombus, parallelogram, kite, and trapezoid. Technically, squares, rectangles, and rhombuses are types of parallelograms.[3]
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.