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 ofSymmetry 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
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