Download Geometry basics: Quadrilaterals [NCS]

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Geometry basics: Quadrilaterals
∗
[NCS]
Free High School Science Texts Project
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†
Creative Commons Attribution License 3.0
1 Quadrilaterals
A
quadrilateral
is any polygon with four sides. The basic quadrilaterals are the trapezium, parallelogram,
rectangle, rhombus, square and kite.
Name of quadrilateral
Figure
trapezium
Figure 1
parallelogram
Figure 2
rectangle
Figure 3
rhombus
Figure 4
square
Figure 5
kite
Figure 6
Table 1:
Examples of quadrilaterals.
1.1 Trapezium
trapezoid. A
isosceles trapezium, where one pair of opposite sides is parallel, the other pair
A trapezium is a quadrilateral with one pair of parallel opposite sides. It may also be called a
special type of trapezium is the
of sides is equal in length and the angles at the ends of each parallel side are equal. An isosceles trapezium
has one line of symmetry and its diagonals are equal in length.
Figure 1:
∗ Version
Examples of trapeziums.
1.1: Aug 5, 2011 1:52 am -0500
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1.2 Parallelogram
A trapezium with both sets of opposite sides parallel is called a
parallelogram.
A summary of the properties
of a parallelogram is:
•
•
•
•
Both pairs of opposite sides are parallel.
Both pairs of opposite sides are equal in length.
Both pairs of opposite angles are equal.
Both diagonals bisect each other (i.e. they cut each other in half).
Figure 2:
An example of a parallelogram.
1.3 Rectangle
A
rectangle
is a parallelogram that has all four angles equal to
90◦ .
A summary of the properties of a
rectangle is:
•
•
•
•
•
Both pairs of opposite sides are parallel.
Both pairs of opposite sides are of equal length.
Both diagonals bisect each other.
Diagonals are equal in length.
All angles at the corners are right angles.
Figure 3:
Example of a rectangle.
1.4 Rhombus
A
rhombus
is a parallelogram that has all four sides of equal length. A summary of the properties of a
rhombus is:
•
•
•
•
•
Both pairs of opposite sides are parallel.
All sides are equal in length.
Both pairs of opposite angles are equal.
Both diagonals bisect each other at
90◦ .
Diagonals of a rhombus bisect both pairs of opposite angles.
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Figure 4:
3
An example of a rhombus. A rhombus is a parallelogram with all sides equal.
1.5 Square
A
square
is a rhombus that has all four angles equal to 90◦ .
A summary of the properties of a square is:
•
•
•
•
•
•
•
Both pairs of opposite sides are parallel.
All sides are equal in length.
All angles are equal to
90◦ .
Both pairs of opposite angles are equal.
Both diagonals bisect each other at
90◦ .
Diagonals are equal in length.
Diagonals bisect both pairs of opposite angles (ie. all
Figure 5:
45◦ ).
◦
An example of a square. A square is a rhombus with all angles equal to 90 .
1.6 Kite
A
kite
is a quadrilateral with two pairs of adjacent sides equal.
A summary of the properties of a kite is:
•
•
•
•
Two pairs of adjacent sides are equal in length.
One pair of opposite angles are equal where the angles are between unequal sides.
One diagonal bisects the other diagonal and one diagonal bisects one pair of opposite angles.
Diagonals intersect at right-angles.
Figure 6:
An example of a kite.
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