Quadrilateral
just means "four sides"
(quad means four, lateral means side).
(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
·
Four sides (edges)
·
Four vertices (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) 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 Square
□ means "right angle" and | 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
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!
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 a 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.
And
a trapezium (UK:
trapezoid) 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!)
|
||
The Kite
It looks like a kite. It has two pairs of sides.
Each
pair is made up of adjacent sides (they meet) 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
Example: a square is also a
rectangle.
So we include a
square in the definition of a rectangle.
(We don't say
"Having all 90° angles makes it a rectangle except when all sides are
equal then it is a square.")
This
may seem odd, as 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:
·
Is a Square a type of Rectangle?
(Yes)
·
Is a Rectangle a type of Kite? (No)
Complex Quadrilaterals
When two sides cross over, you call it a "Complex" or
"Self-Intersecting" quadrilateral like these:
They still have 4 sides, but two sides cross over.
Polygon
A
quadrilateral is a polygon. In fact it is
a 4-sided polygon, just like a triangle is a 3-sided polygon, a pentagon is a
5-sided polygon, and so on.
Play with Them
Now
that you know the different types, you can play with the Interactive Quadrilaterals.
Other Names
A
quadrilateral can sometimes be called:
·
a Quadrangle ("four
angles"), so it sounds like "triangle"
·
a Tetragon ("four and polygon"),
so it sounds like "pentagon", "hexagon", etc.
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