Quadrilaterals: A Quadrilateral Has Four-Sides, It Is 2-Dimensional (A Flat Shape), Closed (The Lines Join

Quadrilaterals
Quadrilateral just means "four sides"

(quad means four, lateral means side).
A Quadrilateral has four-sides, it is 2-dimensional (a flat shape), closed (the lines join
up), and has straight sides.
Properties:
A quadrilateral has:
Four sides (edges)
four vertices (corners)
interior angles that add 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. See below for more details.
Let us look at each type in turn:
The Rectangle
the little squares in each corner mean "right angle"
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 Square
the little squa res in each corner mean "right angle"
A square has equal sides (marked "s") 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 Rhombus
A rhombus is a four-sided shape where all sides have equal length (marked "s").
Also opposite sides are parallel and opposite angles are equal.
Another interesting thing is that the diagonals (dashed lines) meet in the middle at a right
angle. In other words they "bisect" (cut in half) each other at right angles.
A rhombus is sometimes called a rhomb or a diamond.
The Parallelogram
A parallelogram has opposite sides parallel and equal in length. Also 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)
A trapezoid (called a trapezium in the UK) has a pair of opposite sides parallel.
And a trapezium (called a trapezoid in the UK) is a quadrilateral with NO parallel sides:
Trapezoid Trapezium
In the US: a pair of parallel sides NO parallel sides
In the UK: NO parallel sides a pair of parallel sides
(the US and UK definitions are swapped over!)
An Isosceles trapezoid, as shown above, has left and right sides of equal length that join to
the base at equal angles.
The Kite
Hey, it looks like a kite (usually).
It has two pairs of sides:
Each pair is made of two equal-length sides that join up.
Also:
 the angles where the two pairs meet are equal.
 the diagonals, shown as dashed lines above, meet at a right angle.
 one of the diagonals bisects (cuts equally in half) the other.
... and that's it for the special quadrilaterals.
A quadrilateral is a closed plane figure bounded by four line segments. For example, the figure ABCD shown
here is a quadrilateral.
A line segment drawn from one vertex of a quadrilateral to the opposite vertex is called a diagonal of the
quadrilateral. For example, AC is a diagonal of quadrilateral ABCD, and so is BD.
Types of Quadrilaterals and their Properties
There are six basic types of quadrilaterals:
1. Rectangle
 Opposite sides are parallel and equal.

 All angles are 90º.
 The diagonals bisect each other.
2. Square
 Opposite sides are parallel and all sides are equal.

 All angles are 90º.
 Diagonals bisect each other at right angles.
3. Parallelogram
 Opposite sides are parallel and equal.

 Opposite angles are equal.
 Diagonals bisect each other.
4. Rhombus
 All sides are equal and opposite sides are parallel.

 Opposite angles are equal.
 The diagonals bisect each other at right angles.
5. Trapezium
 A trapezium has one pair of opposite sides parallel.

 A regular trapezium has non-parallel sides equal and its base angles are equal, as shown in the following
diagram.
6. Kite
 Two pairs of adjacent sides are equal.

 One pair of opposite angles is equal.
 Diagonals intersect at right angles.
 The longest diagonal bisects the shortest diagonal into two equal parts.
There are six basic types of quadrilaterals:

 Rectangle.
 Square.
 Parallelogram.
 Rhombus.
 Trapezium.
 Kite.
 There are many different kinds of quadrilaterals, but all have several things in
common: all of them have four sides, are coplanar, have two diagonals, and the sum
of their four interior angles equals 360 degrees. This is how they are alike, but what
makes them different?

 We know many quadrilaterals by their special shapes and properties, like squares.
Remember, if you see the word quadrilateral, it does not necessarily mean a figure
with special properties like a square or rectangle! In word problems, be careful not to
assume that a quadrilateral has parallel sides or equal sides unless that is stated.
 Special Quadrilaterals
A parallelogram has two parallel pairs of opposite

sides.
A rectangle has two pairs of opposite sides parallel,
and four right angles. It is also a parallelogram, since
it has two pairs of parallel sides.
A square has two pairs of parallel sides, four right
angles, and all four sides are equal. It is also a
rectangle and a parallelogram.
A rhombus is defined as a parallelogram with four
equal sides. Is a rhombus always a rectangle? No,
because a rhombus does not have to have 4 right
angles.
Trapezoids only have one pair of parallel sides. It's a
type of quadrilateral that is not a parallelogram.
(British name: Trapezium)
Kites have two pairs of adjacent sides that are equal.
Properties of rectangles
A rectangle has three properties:
 All the angles of a rectangle are 90°

 Opposite sides of a rectangle are equal and Parallel
 Diagonals of a rectangle bisect each other

Properties of a square
For a quadrilateral to be a square, it has to have certain properties. Here are the three properties
of squares:
 All the angles of a square are 90°

 All sides of a square are equal and parallel to each other
 Diagonals bisect each other perpendicularly
Properties of parallelogram
A quadrilateral satisfying the below-mentioned properties will be classified as a parallelogram. A

parallelogram has four properties:
 Opposite angles are equal

 Opposite sides are equal and parallel
 Diagonals bisect each other
 Sum of any two adjacent angles is 180°
Properties of rhombus
A rhombus is a quadrilateral which has the following four properties:
 Opposite angles are equal

 All sides are equal and, opposite sides are parallel to each other
 Diagonals bisect each other perpendicularly
 Sum of any two adjacent angles is 180°
Properties of Trapezium
A trapezium is a quadrilateral in which the following one property:
 Only one pair of opposite sides are parallel to each other

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Quadrilaterals

Quadrilateral just means "four sides"

Four sides (edges)

four vertices (corners)

interior angles that add to 360 degrees:

There are special types of quadrilateral:

Let us look at each type in turn:

the little squares in each corner mean "right angle"

A rectangle is a four-sided shape where every angle is a right angle (90°).

the little squa res in each corner mean "right angle"

Also opposite sides are parallel.

A rhombus is sometimes called a rhomb or a diamond.

NOTE: Squares, Rectangles and Rhombuses are all Parallelograms!

The Trapezoid (UK: Trapezium)

In the US: a pair of parallel sides NO parallel sides

In the UK: NO parallel sides a pair of parallel sides

(the US and UK definitions are swapped over!)

Hey, it looks like a kite (usually).

It has two pairs of sides:

Each pair is made of two equal-length sides that join up.

 the angles where the two pairs meet are equal.

 the diagonals, shown as dashed lines above, meet at a right angle.

 one of the diagonals bisects (cuts equally in half) the other.

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

Types of Quadrilaterals and their Properties

There are six basic types of quadrilaterals:

 Opposite sides are parallel and equal.

 Opposite sides are parallel and all sides are equal.

 Opposite sides are parallel and equal.

 All sides are equal and opposite sides are parallel.

 A trapezium has one pair of opposite sides parallel.

 Two pairs of adjacent sides are equal.

There are six basic types of quadrilaterals:

A parallelogram has two parallel pairs of opposite

Kites have two pairs of adjacent sides that are equal.

 All the angles of a rectangle are 90°

 All the angles of a square are 90°

A quadrilateral satisfying the below-mentioned properties will be classified as a parallelogram. A

 Opposite angles are equal

A rhombus is a quadrilateral which has the following four properties:

 Opposite angles are equal

 Only one pair of opposite sides are parallel to each other

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