A **quadrilateral **is a 2-dimensional closed shape with four straight
sides. E.g. The shape *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. *AC* is a
diagonal of quadrilateral *ABCD*, as is *BD*.
Types of Quadrilaterals
There are seven types of quadrilaterals that can be divided into two
groups: **parallelograms** and **other quadrilaterals**.
Parallelograms
Quadrilaterals are called parallelograms if both pairs of opposite sides
are equal and parallel to each other. Different parallelograms and
their properties are described below.
Parallelogram
- Opposite sides of a parallelogram are parallel and equal in length.
- Opposite angles are equal in size.
###### Note:
Rectangle
- Opposite sides of a rectangle are parallel and equal in length.
- All angles are equal to 90°.
Square
- Opposite sides of a square are parallel and all sides are equal in
length.
- All angles are equal to 90°.
Rhombus
- All sides of a rhombus are equal in length
- Opposite sides are parallel.
- Opposite angles of a rhombus are equal.
- The diagonals of a rhombus bisect each other at right angles.
###### Note:
Rectangles, squares and rhombuses (or diamonds) are parallelograms.
Other Quadrilaterals
Other quadrilaterals include trapeziums, kites and irregular
quadrilaterals.
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 diagram.
Kite
- Two pairs of adjacent sides of a kite are equal in length
- One pair of opposite angles (the ones that are between the sides of
unequal length) are equal in size.
- One diagonal bisects the other.
- Diagonals intersect at right angles.
Irregular Quadrilateral
An irregular quadrilateral does not have any special properties.
Angle Sum of a Quadrilateral
Draw a quadrilateral *ABCD*. Then draw the diagonal *AC* to form two triangles.
Finding the Fourth Angle of a Quadrilateral
If the measurements of three angles of a quadrilateral are known, then
the missing angle can be calculated.
Example 21
Find the value of the pronumeral *x* in the accompanying
diagram. Give reasons for your answer.
##### Solution:
Example 22
Find the value of the pronumerals in the following diagram. Give
reasons for your answer.
##### Solution:
Example 23
Find the value of the pronumerals in the following diagram. Give
reasons for your answer.
##### Solution:
Key Terms
quadrilateral, diagonal of a
quadrilateral, parallelogram, rectangle, square, rhombus, trapezium, kite, irregular quadrilateral, angle
sum of a quadrilateral |