# Quadrilateral Classification

A **quadrilateral** is a four-sided closed figure.The origin of the word "quadrilateral" is the two Latin words quadri, a variant of four, and latus, meaning "side."

Quadrilaterals are simple (not self-intersecting) or complex (self-intersecting), also called crossed. Simple quadrilaterals are either convex or concave.

The sum of all angles of a quadrilateral is always 360˚. This is a special case of the $n$-gon interior angle sum formula $(n - 2) \times 180^\circ.$

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## Classification by Sides

Quadrilaterals can be classified on the basis of their sides, giving the following categories:

- Trapezium: no sides the same,
- Isosceles Trapezoid: two opposite sides the same
- Kite: two pairs of sides the same
- Rhombus: all sides the same

Here is an interesting chart, showing family of quadrilaterals:

## Classification by Angles and Parallels

Quadrilaterals are also commonly classified by their angles and parallel sides:

**Parallels**

- Trapezoid: one pair of sides parallel
- Parallelogram: both pairs of sides paralllel

**Angles**

- Rectangle: all angles are right angles (rectangles are always also parallelograms).

## Squares

A square, based on the criteria above, is both a rhombus and a rectangle and has all the properties of both of those shapes.

## Cyclic Quadrilaterals

A quadrilateral may be cyclic. If opposite angles are supplementary, all its vertices will lie on the circumference a circle, called the *circumcircle*.

**Cite as:**Quadrilateral Classification.

*Brilliant.org*. Retrieved from https://brilliant.org/wiki/quadrilateral-classification/