POLYGONS

POLYGONS

 A) Recognising Polygons 

A polygon is a plane figure with 3 or more straight edges as its sides.

For example :-

(a)                       (b)

(a) and (b) are polygons.

(c)                        (d)

(c) and (d) are not polygons.

B) Names Of Polygons

A polygon is named after the number of sides it contains. The following names are given to some common polygons.

In general, a polygon with n sides is called a “n-gone”

For example :-

a polygon with 12 sides is called a 12-gon

 

Worked Example 1

Name the following polygons

(a)

(b)    

 

C) Determining The Number Of Sides, Vertices and Diagonals In A Given Polygons

1) A vertex is the point where two straight lines meet.

2) A diagonal is a straight line joining two vertices which are not adjacent to each other.

For example :-
The quadrilateral KLMN contains
(i) 4 sides (i.e. KL, LM, MN and KN)
(ii) 4 vertices (i.e. K, L, M and N)
(iii) 2 diagonals (i.e. KM and LN)
Worked Example 2
State the number of
(i) sides, (ii) vertices, (iii) diagonals
in each of the following polygons
(a) (b)

3) The table below shows the number of sides, vertices and diagonals for some common polygons

D) Sketching Polygons

To sketch a polygon, determine the number of sides or vertices the polygon has first.

Worked Example 3

Sketch two different shapes to represent the following polygons

(a) quadrilateral

(b) hexagon

Solution

(a)

(b)

SYMMETRY

A) Determining and Drawing The Line (s) Of Symmetry Of Shapes

1)  An object is said to have a line of symmetry if it can be divided into identical halves when it is folded along that line.

For example :-

(a)

(b)

2) An object may have more than one line of symmetry

For example :-

(a)

Worked Example 4

Determine whether each of the following object has a line of symmetry

(a)            (b)

Solution

Worked Example 5

Draw and state the number of line(s) of symmetry in aech of the following object

(a)     (b)

Solution

(a)    1 line of symmetry

 (b)     2 lines of symmetry

Worked Example 6

The figure below are drawn on square grids. Draw and state the number of lines of symmetry in each figure

(a)  (b)

Solution

(a)  2 lines of symmetry

 (b)  4 lines of symmetry

Worked Example 7

 The figure below are drawn on tessellation of equilateral triangles. Draw and state the number of lines of symmetry in each figure.

(a)  (b)

Solution

(a) 2 lines of symmetry

(b) 1 line of symmetry

B) Completing A Given Shape

When the line of symmetry of an incomplete shape is given, the shape can be completed by using the concept of symmetry

(a)   (b)

Solution

(a)    (b)

(a)   (b)

Solution

(a)   (b)

C) Drawing Designs Using The Concept Of Symmetry 

(a)  (b)

Solution

Below are two possible designs

(a)  (b)

(a)   (b) 

Solution

(a)      (b)  

TRIANGLES

A triangle is a polygon which has 3 sides

For example :-

A) Recognising Different Types Of Triangles and Their Geometric Propertie

1) Triangles can be classified according to:

  • the number of equal sides

  •  the types of angles

(a)     (b)

(a)  (b)  (c)

B) Determining and Drawing Lines of Symmetry of Given Triangles

1) The number of lines of symmetry in a triangle can be determined by folding the triangle.

For example :-

a) an isosceles triangle has 1 line of symmetry

b) an equilateral triangle has 3 lines of symmetry

c) a scalene has no line of symmetry

(a)   (b) (c) 

Solution

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