# Geometry/Quadrilaterals

A quadrilateral is a polygon that has four sides.

## Special Types of Quadrilaterals

* Parallelogram
** A parallelogram is a quadrilateral having two pairs of parallel sides.
** The two opposite sides are equal.
** Opposite angles are equal.
* Rhombus
** A rhombus is a quadrilateral of which all four sides are the same length.
* Rectangle
** A rectangle is a parallelogram of which all four angles are 90 degrees.
* Square
** A square is a quadrilateral of which all four sides are of the same length, and all four angles are 90 degrees.
* Trapezoid
** A trapezoid is a quadrilateral which has two parallel sides (U.S.)
* Trapezium
** U.S. usage: A trapezium is a quadrilateral which has no parallel sides.
** U.K usage: A trapezium is a quadrilateral with two parallel sides (same as US trapezoid definition).
* Kite
** A kite is an quadrilateral with two pairs of congruent adjacent sides.
One of the most important properties used in proofs is that the sum of the angles of the quadrilateral is always 360 degrees. This can easily be proven too:
If you draw a random quadrilateral, and one of its diagonals, you'll split it up into two triangles. Given that the sum of the angles of a triangle is 180 degrees, you can sum them up, and it'll give 360 degrees.

### Navigation

* Geometry
* Part I—Euclidean Geometry:
** Chapter 1. Geometry/Points, Lines, Line Segments and Rays
** Chapter 2. Geometry/Angles
** Chapter 3. Geometry/Properties
** Chapter 4. Geometry/Inductive and Deductive Reasoning
** Chapter 5. Geometry/Proof
** Chapter 6. Geometry/Five Postulates of Euclidean Geometry
** Chapter 7. Geometry/Vertical Angles
** Chapter 8. Geometry/Parallel and Perpendicular Lines and Planes
** Chapter 9. Geometry/Congruency and Similarity
** Chapter 10. Geometry/Congruent Triangles
** Chapter 11. Geometry/Similar Triangles
** Chapter 12. Geometry/Quadrilaterals
** Chapter 13. Geometry/Parallelograms
** Chapter 14. Geometry/Trapezoids
** Chapter 15. Geometry/Circles/Radii, Chords and Diameters
** Chapter 16. Geometry/Circles/Arcs
** Chapter 17. Geometry/Circles/Tangents and Secants
** Chapter 18. Geometry/Circles/Sectors
** Appendix A. Geometry/Postulates & Definitions
** Appendix B. Geometry/The SMSG Postulates for Euclidean Geometry
* Part II—Coordinate Geometry:
** Geometry/Synthetic versus analytic geometry
* Two and Three-Dimensional Geometry and Other Geometric Figures
** Geometry/Perimeter and Arclength
** Geometry/Area
** Geometry/Volume
** Geometry/Polygons
** Geometry/Triangles
** Geometry/Right Triangles and Pythagorean Theorem
** Geometry/Polyominoes
** Geometry/Ellipses
** Geometry/2-Dimensional Functions
** Geometry/3-Dimensional Functions
** Geometry/Area Shapes Extended into 3rd Dimension
** Geometry/Area Shapes Extended into 3rd Dimension Linearly to a Line or Point
** Geometry/Polyhedras
** Geometry/Ellipsoids and Spheres
** Geometry/Coordinate Systems (currently incorrectly linked to Astronomy)
* Traditional Geometry:
** Geometry/Topology
** Geometry/Hyperbolic and Elliptic Geometry
** Geometry/Projective Geometry
** Geometry/Neutral Geometry
** Geometry/Inversive Geometry
* Modern geometry
** Geometry/Unified Angles
** Geometry/Groups
** Geometry/Algebraic Geometry
** Geometry/Differential Geometry
** Geometry/Algebraic Topology
** Geometry/Noncommutative Geometry
* Geometry/An Alternative Way and Alternative Geometric Means of Calculating the Area of a Circle