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 $(n - 2) \times 180^\circ.$

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:

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).

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

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