INVESTIGATE THE SUM OF THE ANGLES OF A POLYGON
1)
In your own words, write down the meaning of the word polygon.
2)
Draw a triangle.
Write down the sum of its angles.
3)
Draw a quadrilateral.
Draw a line from one vertex to the opposite vertex so as to separate the quadrilateral
into two triangles.
Write down the sum of its angles.
(Hint: The sum of the angles of two triangles is the same as the sum of the angles of
a quadrilateral.)
4)
Draw a pentagon.
Divide the pentagon into a minimum number of triangles, and use this to write down the
sum of its angles.
5)
Copy and complete the following table:
Number
sides
3
4
5
6
7
of Name
polygon
of Number
triangles
of Sum
of
angles
the
(Draw the shapes only if you need to.)
6)
Add an extra row to your table, and use this to predict what you think will happen for
an eight-sided shape.
7)
Draw the eight-sided shape and check your prediction.
8)
Write about any patterns that you notice.
For example, the sum of the angles, the number of triangles, etc.
9)
In words, write down the rule for working out the sum of the angles from the number
of sides.
10 )
Use this rule to help you find the sum of the angles of a 20-sided polygon.
Show your working out.
11 )
Using 'n' to represent the number of sides of the polygon, and write your rule using
algebra.