Notes

CHAPTER 10: Polygons


Learning Objectives

• Recognize, name and sketch polygons.
• Determine the numbers of sides, vertices and diagonals of given polygons.
• Determine and draw the line(s) of symmetry of shapes.
• Complete shapes given part of the shapes and the lines of symmetry.
• Draw triangles or quadrilaterals using a protractor and a ruler.
• State the geometric properties of different types of triangles and quadrilaterals and name the triangles and the quadrilaterals.
• Determine the sum of the angles of a triangle and a quadrilateral.
• Solve problem involving triangles and quadrilaterals.

10.1 Polygons

1. Polygons are closed plane figures bounded by three or more straight lines.

2. The name of polygons depends on the number of sides or number of vertices.

3. Diagonals are straight lines joining two vertices which are not adjacent of a polygon.
    For example, a rectangle has 2 diagonals.

4. A polygon of n sides has n(n-3)/2 diagonals.

Example 1

Which of the following is a polygon?

Solution:

(a) Polygon

(b) Not polygon

(c) Not polygon

(d) Polygon

Example 2

Name the polygon below and state how many vertices and diagonals does it have.

Solution:

a) Name = pentagon
Number of vertices = 5                           

Number of diagonals = (5(5-3))/2 = 5

b)Name = octagon
Number of vertices = 8

Number of diagonals = (8(8-3))/2 = 20

Effective Notes

1. 

Polygon	Number of sides
Triangle	3
Quadrilateral	4
Pentagon	5
Hexagon	6
Heptagon	7
Octagon	8
Nonagon	9
Decagon	10

2.

Types of triangles	Properties
a) Equilateral triangle	3 equal sides         3 equal angles     3 axes of symmetry
b) Isoceles triangle	2 equal sides         2 equal angles         1 axis of symmetry
c) Scalene triangle	All sides are unequal         All angles are unequal
d) Obtuse-angled triangle	It has one obtuse angle (90º < x < 180º)
e) Right-angled triangle	It has one right angle
f) Acute-angled triangle	All the angles, x, y and z, are acute angles (< 90º)

3.

Types of quadrilaterals	Properties
a) Rectangle	Opposite sides are equal          All angles are 90º     2 axes of symmetry
b) Square	All sides are equal         All angles are 90º        4 axes of symmetry
c) Parallelogram	Opposite sides are equal and parallel         Opposite angles are equal
d) Rhombus	All sides are equal and opposite parallel sides are          Opposite angles are equal
e) Trapezium	A pair of parallel sides with unequal lengths.

4. The sum of angles of a triangle = 180 º

       

5. The exterior angle of a triangle is equal to the sum of the two opposite interior angles.

         

6. The sum of angles of a quadrilateral = 360 º