Quadrilaterals

Quadrilateral just means "four sides"
(quad means four, lateral means side).
Any four-sided shape is a Quadrilateral.
But the sides have to be straight, and it has to be 2-dimensional.

Properties

Four sides (or edges)
Four vertices (or corners).
The interior angles add up to 360 degrees:

Try drawing a quadrilateral, and measure the angles. They should add to 360°

Types of Quadrilaterals

There are special types of quadrilateral:

Some types are also included in the definition of other types! For example a square, rhombus and rectangle are also parallelograms.

Let us look at each type in turn:

The Rectangle


		means "right angle"
	and	show equal sides

A rectangle is a four-sided shape where every angle is a right angle (90°).
Also opposite sides are parallel and of equal length.

The Rhombus

A rhombus is a four-sided shape where all sides have equal length.

Also opposite sides are parallel and opposite angles are equal.

Another interesting thing is that the diagonals (dashed lines in second figure) of a rhombus bisect each other at right angles.

The Square


		means "right angle"
		show equal sides

A square has equal sides and every angle is a right angle (90°)
Also opposite sides are parallel.
A square also fits the definition of a rectangle (all angles are 90°), and a rhombus (all sides are equal length).

The Parallelogram

Opposite sides are parallel and equal in length, and opposite angles are equal (angles "a" are the same, and angles "b" are the same)

NOTE: Squares, Rectangles and Rhombuses are all Parallelograms!

Example:

A parallelogram with:

all sides equal and
angles "a" and "b" as right angles

is a square!

The Trapezoid (UK: Trapezium)


Trapezoid	Isosceles Trapezoid

A trapezoid (called a trapezium in the UK) has one pair of opposite sides parallel.
It is called an Isosceles trapezoid if the sides that aren't parallel are equal in length and both angles coming from a parallel side are equal, as shown.

Language Note: In the US a "trapezium" is a quadrilateral with NO parallel sides!

The Kite

Hey, it looks like a kite. It has two pairs of sides. Each pair is made up of adjacent sides that are equal in length. The angles are equal where the pairs meet. Diagonals (dashed lines) meet at a right angle, and one of the diagonal bisects (cuts equally in half) the other.

... and that's it for the special quadrilaterals.

Irregular Quadrilaterals

The only regular quadrilateral is a square. So all other quadrilaterals are irregular.

The "Family Tree" Chart

Quadrilateral definitions are inclusive.

Example: a square is also a rectangle.

So we include a square in the definition of a rectangle.
(We don't say "A rectangle has all 90° angles, except if it is a square")

This may seem odd because in daily life we think of a square as not being a rectangle ... but in mathematics it is.
Using the chart below you can answer such questions as: