# Quadrilaterals: Classification

A
**
quadrilateral
**
is a
polygon
with four sides.

There are many special types of quadrilateral.

A
**
parallelogram
**
is a quadrilateral in which both pairs of opposite sides are
parallel
.

A parallelogram also has the following properties:

- Opposite angles are congruent;
- Opposite sides are congruent;
- Adjacent angles are supplementary;
- The diagonals bisect each other.

A
**
rectangle
**
is a parallelogram with four right angles, so all rectangles are also parallelograms and quadrilaterals. On the other hand, not all quadrilaterals and parallelograms are rectangles.

A rectangle has all the properties of a parallelogram, plus the following:

- The diagonals are congruent.

A
**
rhombus
**
is a parallelogram with four
congruent
sides. The plural of rhombus is
**
rhombi
**
. (I love that word.)

A rhombus has all the properties of a parallelogram, plus the following:

- The diagonals intersect at right angles.

A
**
square
**
can be defined as a rhombus which is also a rectangle – in other words, a parallelogram with four congruent sides and four right angles.

A
**
trapezoid
**
is a quadrilateral with exactly one pair of parallel sides. (There may be some confusion about this word depending on which country you're in. In India and Britain, they say
**
trapezium
**
; in America, trapezium usually means a quadrilateral with no parallel sides.)

An
**
isosceles trapezoid
**
is a trapezoid whose non-parallel sides are congruent.

A
**
kite
**
is a quadrilateral with exactly two pairs of adjacent congruent sides. (This definition excludes rhombi. Some textbooks say a kite has at least two pairs of adjacent congruent sides, so a rhombus is a special case of a kite.)

A
**
scalene
**
quadrilateral is a four-sided polygon that has no congruent sides. Three examples are shown below.

## Venn Diagram of Quadrilateral Classification

The following Venn Diagram shows the inclusions and intersections of the various types of quadrilaterals.

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