MATHEMATICS - FORM 1

POLYGONS

                   


POLYGONS


A) Recognising Polygons

A polygon is a plane figure with three 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

1. A polygon is named after the number of

    sides it contains. The following names

    are given to some common polygons.

   

2. 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 Polygon


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) 40vertices (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 each of the following object.

(a)                       (b)
                

Solution

(a)                      (b)
          

     1 line of             
2 lines of 
    symmetry            symmetry

Worked Example 6

The figurs 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 symmmetry

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





(a)
     

(b)

     

Solution

(a)
     

(b)
     



(a)                           (b)
              

Solution

(a)                           (b)
                

C) Drawing Designs using the
 Concept of Symmetry






(a)                          (b)
           

Solution

Below are two possinble designs.

(a)
      

(b)
      



(a)                            (b)
               

Solution

(a)                            (b)
               

10.3 TRIANGLES



     

A) Recognising Different Types of Triangles
 and their Geometric Properties

   

               

         (ii)
               

         (iii)
               

(b) The types of angles

         



(a)                         (b)
             





(a)                        (c)
              

(b)       
     



B) Determining and Drawing Lines
of Symmetry of given Triangles




           

   



(a)                       (c)
              

(b)
     

Solution



C) Drawing Triangles





Solution

Step 1

Skretch the triangle.

         

Step 2

Draw EF = 2 cm.

       

Step 3

Using a protractor, draw an angle of 50 at F.

       

Step 4

Using a ruler, mark the point G 1 from F.

       

Step 5

Join EG

       



Solution

Step 1

Sketch the triangle.

     

Step 2

Draw JK = 3 CM.

   

Step 3

Using a protractor, draw an angle of 30 at J.

     

Step 4

Using a ruler, mark the point L 1.5 cm from K.

   

Step 5

Join KL.

   




     



     



     



   



   

D) Determining the Sum of Angles of a Triangle











E) Determining the Angles of an Equilateral Triangle





(a)                            (b)
         





             

F) Determining Wheter the two Base Angles of an
 Isosceles Triangle are Equal










G) Determining the Exterior and Interior
 Opposite Angles of a Triangle

     










H) Problem Solving involving Triangle
 










10.4 QUADRILATERALS



A) Recognising Different Types of Quarilaterals
 and their Geometric Properties




               



             



               



                   



             
B) Determining and Drawing Lines of
 Symmetry of given Quadrilaterals



           



          



          



C) Drawing Quadrilaterals





           



         



           



            



             











































D) Determining the Sum of Angles
of a Quadrilateral







         

E) Determining whether the Opposite
Angles of a Parallelogram are Equal











F) Problem Solving involving Quadrilateral