GR 9 3-5-8 LEARNERS
Page 1 of 2
NAME:
Gr 9
Date:
Time
1 hr.
CAPS
3-5 Construction of Geometric Figures By construction explore
Reference the sum of the interior angles of polygons
3-5-8 Explore the sum of the interior angles of polygons
Topic
1.
Think First! [10 mins]
What is a polygon?
Many English words have their roots in other languages.
Polygon is a word made from two Greek words: polys "many" + gonia "angle"
So a polygon is a shape with many angles.
Some polygons have special names.
1.1
Match the names of the polygons in the box below with the number of angles in the
polygon.
decagon, heptagon, hexagon, nonagon, octagon, pentagon, quadrilateral, triangle
Number
of angles
Sketch of
Shape
3
Name of
shape
Triangle
Number
of sides
Number
of angles
4
Square
8
5
Pentagon
9
6
Hexagon
10
Sketch of
Shape
Name of Number
shape
of sides
7
1.2
What do you notice about the number of angles and the number of sides in each shape?
1.3
What is the difference between a regular polygon and an irregular polygon?
1.4
What is the special name given to a regular quadrilateral?
1.5
What is the special name given to a regular triangle?
2.
Go ahead! [20 mins]
Draw each of the following polygons following the given instructions:
2.1
An equilateral triangle using compass and ruler
2.2
A square by using your compass and a ruler
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GR 9 3-5-8 LEARNERS
2.3
2.4
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An irregular pentagon using your ruler and a pencil.
A regular hexagon using your compass and a ruler using the method described below.
Draw a circle with a
suitable radius
Keeping exactly the same radius as
the circle, use your compass to
draw arcs on the circumference of
the circle 1 radius width away
from each other.
Join the points of
intersection to form a
regular hexagon.
2.5
Draw 7, 8, 9 and 10 sided polygons using any method of your choice.
Make sure the lines are straight.
2.6
Divide each of the polygons you drew in 2.4 and 2.5 above into triangles as shown below.
3.
Check your work! [5 mins]
4.
Think Again! [10 mins]
4.1
Copy and complete this table by using different the polygons you have drawn 2 above.
Number of sides of polygon (n)
Number of triangles inside the polygon
Total sum of angles of triangles
3
4
5
6
7
8
9
10
4.2
4.3
4.4
4.5
Write a rule to calculate the sum of the angles of a polygon with any number of sides.
Use your rule to calculate the sum of the angles of an octagon.
Use your rule to calculate the sum of the angles of a decagon.
Use your rule to calculate the sum of the angles of 25 sided polygon.
5.
Going further! [15 mins]
5.1.
Investigate the sum of the exterior angles of a polygon.
Do this by extending each side in one direction and measuring the exterior angle.
Find the sum. The conclusion will surprise you.
Use this fact to make a new formula for finding the interior angles of a regular polygon.
5.2
5.3
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www.e-classroom.co.za