BLUEBELL INTERNATIONAL SECONDARY SCHOOL
10 LK Anga Rd, Off Peter Odili Rd, Trans Amadi Industrial Layout, Port Harcourt,
Rivers State.
7
AUTUMN TERM, 2022/2023 ACADEMIC SESSION
1
SCHEME OF WORK FOR AUTUMN TERM 2022/2023 SESSION
WK
TOPIC
1.
Introduction to Geometry
2.
Measuring, Drawing and Construction of Angles.
3.
Angles in a triangle I
4.
Angles in a triangle II
5.
Angles in a triangle III
6
MID TERM TEST/BREAK
7
Construction of triangles I
8.
Construction of triangles II
9.
Plane shapes I
10.
Plane shapes II
11.
Revision
12.
Examination
13.
Closing
2
WEEK 1
DATE:
CLASS: YEAR 7
TOPIC: INTRODUCTION TO GEOMETRY
LEARNING OBJECTIVES: By the end of the lesson, the students should be able to:
i. define lines and angles.
ii. identify angles between two lines.
iii. interpret angle as a measure of rotation and its measurement in terms of revolution.
iv. convert angles to time and vice versa.
A. LINES AND ANGLES
a. Lines:
A line can be described as a straight path joining two points A and B. It has end points
and a definite length.
A
B
Types of Lines:
Intersecting Lines:
Two lines having a common point are called intersecting lines. The common point is
known as the point of intersection. See the figure below:
O
D
Parallel lines:
Lines that remain the same distance apart forever are called parallel lines. See the figure
below:
A
B
C
D
3
Concurrent Lines:
If two or more lines intersect at the same point, then they are known as concurrent
lines. See this figure here:
A
D
F
E
C
B
Transversal:
A Transversal is a line that intersects two or more lines (in the same plane). The lines
can be parallel or non-parallel.
Non-parallel lines
Parallel lines
CLASSWORK:
1. What is a line?
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------2. Explain the following type of lines
i. Transversal:
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ii. Parallel lines:
4
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------iii. Intersecting lines:
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------b. Angles:
When two or more lines meet at a common points, angle(s) is/are formed.
Angles are grouped into different types, depending on their sizes.
i. Acute Angle: This is an angle greater than 00 but less than 900
ii. Obtuse angle: This is an angle greater than 900 and less than 1800
iii. Right angle: A right angle is an angle equal to 900
5
iv. Reflex angle: This is an angle greater than 1800 and less than 3600
HOMEWORK:
Explain the following types of angles:
i. Acute angle:
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ii. Obtuse angle:
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------iii. Reflex angle:
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------v. Adjacent angles: When two angles lie beside each other and have a common vertex,
we say they are adjacent to each other. In the figure below, AOB is adjacent to BOC.
BOC is adjacent to AOB.
A
B
C
O
6
vi. Angles about a point: Angles about a point sum up to 360 0
ao
bo
c
o
From the figure above, ao + bo + co +do = 3600
vii. Vertically opposite angles:
bo
a
o
co
o
d
Vertically opposite angles are equal, hence: a = c; b = d
viii. Angles on a straight line: Angles on a straight line sum up to 1800
ao
bo
a o + bo + co = 1800
co
ix. Alternate angles: When a transversal intersects a line, alternate angles can be seen.
Alternate angles lie on opposite sides of the transversal line and on opposite sides of the
other lines. The diagrams below shows alternate angles when the lines are parallel.
7
xi. Corresponding angles: Corresponding angles are angles that are in an ‘F’ position.
Corresponding angles are in the same location at the intersection of the lines with the
transversal.
Note:
Complementary angles: Complementary angles are angles are angles that add up to 90 0.
Supplementary angles: Supplementary angles add up to 180 0. These angles do not
necessarily need to be adjacent.
C.SOLVED EXAMPLES ON ANGLES BETWEEN LINES
1. Find the unknown angles in each of the following.
470
b
1330
a
550
c
1500
250
Solution:
1. a = 470 because the angles are vertically opposite
b = 1330 because it is vertically opposite to angle 1330
c = 3600 – 1500 – 250 - 550 because the angles are formed around a point.
c = 1300
8
2. Consider the diagram below:
Y
W
950
700
S
150
T
700 + 950 + 150 = 1800: angles on a straight line. The angles are supplementary
3. Determine the values of the unknown angles.
490
m
200
1000
x
Solution:
m = 1800 – 490 = 1310 because the angles are on a straight line
x = 1800 – 200 – 1000 = 600 because the angles are on a straight line
4. In the diagrams below, find the size of the unknown angles.
a.
570
d
e
Solution:
Always start with the known angle. In this case, it is 570. Always try to solve the
unknown angles in alphabetical order.
This angle is alternate with e, so e is also 570
Angles d and e are on a straight line, so they add up to 1800. Therefore, angle d is 1230
9
Now, solve this!
A
1.
C
107
t
0
s
B
D
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------2. Find the unknown angles.
630
m
n
m
1450
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------10
3. Find the lettered angles in the figure below.
f
g
d
e
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------11
HOMEWORK:
Find the lettered angles given in the figures below:
510
450
y
300
x
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------12
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------D. ANGLE AND TIME:
The word ‘angle is used for amount of turn. For example, Fig 1 below shows how the
hands of a clock move between 9 o’clock and 10 o’clock.
Both hands turn. In one hour, the amount that each hand turn is different. The
minute hand makes one complete turn, or one revolution. The angle turned = 1
revolution
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The hour hand turns through
turned =
of 1 revolution. From the figure below, the angle
𝑡ℎ revolution.
It is obvious now that just as we can measure length, so we can measure angle. To
avoid fractions, one revolution is divided into 360 equal parts. Each part is called a
degree. The symbol 0 is used for representing degree.
1 revolution = 360 degrees or 3600
10 =
revolution
Examples:
1. What is the angle between the hour hand and the minute hand of a clock at 8
o’clock?
Solution: The angle between the hands is the amount that one hand must turn to
reach the position of the other. Consider the figure above. That is of a revolution.
Angle between hands =
of a revolution =
𝑜𝑓 360 = 120 .
Notice, in the above example, that the size of the angle does not depend on the size of
the hands.
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CLASSWORK:
1. What is the angle between the hour hand and the minute hand of a clock at 5
minutes to 12 o’clock?
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------2. Find the smaller angles between the hour hand and the minute hand of a clock at
the following times. Give your answer in degrees.
a)
past 3
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------b)
past 5
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------HOMEWORK:
1. Find the smaller angles between the hour hand and the minute hand of a clock at
the following times. Give your answers both in revolutions and in degrees
a) 2 o’ clock
b) 3 o’ clock
c) 11 o’ clock
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d) 5 o’clock
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------16
WEEK 2
DATE:
CLASS: YEAR 7
TOPIC: NAMING, MEASURING AND CONSTRUCTION OF ANGLES
LEARNING OBJCTIVES: By the end of the lesson, the students should be able to:
i. name angles using capital letters.
ii. measure a given angle to the nearest degree using a protractor.
iii. construct angles
A. NAMING OF ANGLES:
When lines OA and OB meet at the point O (look at the figure below), we say that angle
AOB or angle BOA is the angle between them. AOB is short for angle AOB. Notice that
O, the middle letter, is the vertex of the angle. The lines OA and OB are the arms of
the angle.
If OA is fixed and OB can turn, we get angles of different sizes. Some of these have
special names. This has been discussed in a previous lesson.
B. MEASURING ANGLES:
A protractor is used to measure the number of degrees in an angle. To measure an
angle:
i. Place the protractor over the angle so that its centre, O, is exactly over the vertex of
the angle and the base line is exactly along one arm of the angle.
ii. Count the degrees from the base line to the other arm of the angle. Most protractors
have two rows of numbers. This is because, you can measure the angle either
anticlockwise or clockwise.
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CLASSWORK:
Measure the size of the following angles shown below with a protractor:
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------HOMEWORK:
1. Say whether each of the following angles is acute, obtuse or reflex.
a. 930 _____________________________________________________________________________
b. 1750 ____________________________________________________________________________
c. 860 _____________________________________________________________________________
d. 1910 ____________________________________________________________________________
e. 2110 ____________________________________________________________________________
f. 720 ______________________________________________________________________________
2. Estimate the sizes of the angles shown below to the nearest 100
a.
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b.
c.
Constructions are accurate drawings of geometric figures. Here, you will be guided
through on how to construct perpendicular bisectors and lines perpendicular to a
point, copy an angle of a given size.
C. CONSTRUCTION OF ANGLES:
a. To bisect a straight line:
i. Draw a line segment AB
ii. Open a pair of compasses so that the radius is about
of the length of AB
iii. Place the sharp point of the compass on A. Draw two arcs, one above, the other
below the middle of AB.
iv. Keep the same radius and place the sharp pint of the compass on B. Draw two arcs
so that they cut the first arcs at P and Q.
v. Draw a straight line through P and Q so that it cuts AB at M. PQ is the
perpendicular bisector of AB.
19
b. To construct an angle of 900
i. Draw line AC and locate a point B on the line.
ii. With centre B and any radius, draw arcs to cut AC at P and Q
iii. With centres P, Q and equal radii, draw arcs to cut each other at R
iv. Join BR
c. To construct an angle of 600
i. Draw a given line BC
ii. With centre B and any radius, draw an arc to cut BC at X
iii. With centre X and the same radius as in ‘ii’ above, draw an arc to cut the first arc
at A.
iv. Join AB.
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HOMEWORK
Construct the following angles i. 300 ii. 450
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WEEK 3
DATE:
CLASS: YEAR 7
TOPIC: ANGLES IN A TRIANGLE 1
LEARNING OBJECTIVES: By the end of the lesson, the students should be able to:
i. define a triangle as a plane shape.
ii. state at least three types of triangles.
iii. describe briefly an equilateral triangle, isosceles triangle, scalene triangle and a
right angled triangle.
iv. state at least three properties of each of the triangles mentioned in ‘iii’ above.
A. DEFINITION OF A TRIANGLE:
A triangle is a three sided polygon that consists of three edges and three vertices. It is
a two dimensional shape. If ABC is a triangle, then it is denoted as ∆ABC, where A, B,
C are the vertices of the triangle.
B. GENERAL PROPERTIES OF A TRIANGLE:
Let us discuss here, some of the properties of triangles.
i. A triangle has three sides and three angles.
ii. The sum of the angles of a triangle is always 180 degrees.
iii. The exterior angles of a triangle always add up to 3600
iv. The sum of consecutive interior and exterior angle is supplementary.
C. TYPES OF TRIANGLES:
On the basis of length of the sides, triangles are classified into three categories:
i. Scalene Triangle
ii. Isosceles Triangle
iii. Equilateral Triangle
On the basis of measurement of the angles, triangles are classified into three
categories:
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i. Acute angle Triangle
ii. Right Angle Triangle
iii. Obtuse Angle Triangle.
EQUILATERAL TRIANGLE:
This is a triangle that has all its sides equal in length. Since the three sides are equal,
therefore, the three angles, opposite to the equal sides, are equal in measure. It can
also be called equiangular triangle.
Note that the shape of an equilateral triangle is regular.
Properties of Equilateral Triangle:
i. All three sides are equal
ii. All three angles are congruent and are equal to 60 degrees.
iii. It is a regular polygon with three sides.
iv. The perpendicular drawn from vertex of the equilateral triangle to the opposite side
bisects it into equal halves.
v. In an equilateral triangle, median, angle bisector and altitude for all sides are all the
same.
ISOSCELES TRIANGLE:
An isosceles triangle definition states it a a polygon that consists of two equal sides,
two equal angles, three edges, three vertices and the sum of internal angles of a
triangle equal to 1800.
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Properties of an isosceles triangle:
i. Two sides are congruent to each other.
ii. The third side of an isosceles triangle which is unequal to the other two sides is
called the base of the isosceles triangle.
iii. The two angles opposite to the equal sides are congruent to each other. That means
it has two congruent base angles.
iv. The angle which is not congruent to the two congruent base angles is called the
vertex angle.
v. The altitude from the vertex of an isosceles triangle bisects the base into two equal
parts and also bisects its vertex angle into two equal parts.
SCALENE TRIANGLE:
This is a triangle that has all its sides of different lengths. This means all the sides of a
scalene triangle are unequal and all the three angles are also of different measures.
Properties of a scalene triangle:
Some of the important properties of the scalene triangle are as follows:
i. It has no equal sides.
ii. It has no equal angles
iii. It has no line of symmetry
iv. It has no point symmetry
v. The angles inside this triangle can be an acute, obtuse or right angle.
RIGHT ANGLED TRIANGLE:
A right angled triangle is a triangle, that has one of its interior equal to 90 degrees or
any one angle is a right angle.
24
Some of the properties of Right Angle Triangle include:
i. One angle is always 900 or right angle
ii. The side opposite angle 900 is the hypotenuse
iii. The hypotenuse is always the longest side
iv. The sum of the other two interior angles is equal to 900.
v. The other two adjacent to the right angle are called base and perpendicular.
CLASSWORK:
1. Define a triangle.
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------2. Describe the following types of triangles.
a. Equilateral triangle
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------b. Isosceles triangle
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------25
c. Scalene triangle
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------HOMEWORK:
Outline three properties each of the following types of triangles
a. Right Angle Triangle
b. Isosceles Triangle
c. Equilateral Triangle
d. Scalene Triangle
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------26
WEEK 4
DATE:
CLASS: YEAR 7
TOPIC: ANGLES IN A TRIANGLE II
LEARNING OBJECTIVES: By the end of the lesson, the students should be able to:
i. solve problems on the calculation of angles of triangles.
Note that tri – angles means three triangles.
Examples:
State the sizes of the lettered angles in the figures below.
a.
a0 + 600 + 300 = 1800 (Sum of angles
in a triangle)
a0
a o + 900 = 1800
600
a o = 1800 – 900 = 90
300
b.
The triangle is an isosceles triangle
f
Therefore, base angles are same.
e = 75
e + f + 75 = 1800 (angle sum in a triangle)
750
e
o
f + 75 +75 = 180 0; f + 150 = 1800; f = 30
CLASSWORK:
1. Calculate the third angle of a triangle in which two of the angles are as follows:
a. 470 and 650
b. 240 and 770
c. 560 and 180
d. 390 and 210
e. each 580
f. 1030 and 420
27
g. 690 and 460
h. 380 and 710
I 350 and 550
j. 580 and 250
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------28
2. The angles in the table 4.1 below refer to the diagram in fig. 4.1. Calculate the
missing angles in each row.
A
B
D
C
Fig 4.1.
ABC
580
650
BAC
470
ACB
ACD
1180
860
190
460
350
Table 4.1
HOMEWORK:
In fig. 4.2, ABC = x0, BAC is twice as big as ABC. ACB is three times as big as ABC.
a. Make an equation in x. Solve the equation.
b. Find the three angles of the triangle.
C
B
X0
A
Fig. 4.2
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------29
WEEK 5
DATE:
CLASS: YEAR 7
TOPIC: ANGLES IN A TRIANGLE III
LEARNING OBJECTIVES: By the end of the lesson, the students should be able to:
i. solve harder calculations on triangles.
Examples:
1. State the sizes of the lettered angles in the figures below. Note that in any diagram,
lines marked with small line are equal in length.
a.
a0
c0
400
1200
Solution:
c0 + 1200 = 1800 (angle on a straight line)
c = 1800 – 1200 = 60
400 + a + c = 1800 (angle sum in a triangle)
400 + a + 600 = 1800
a = 180 – (40 +60)
a = 180 – 100
a = 80
b.
500
l0
m0
n0
p0
q0
30
Solution:
l = m = 650 (sum of the angles of an isosceles triangle)
p = n = 650 (alternate to l and m respectively)
q = 500 (sum of the angles of a triangle is 1800)
CLASSWORK:
State the sizes of the lettered angles in the figures below
a.
f0
v0
u0
250
650
bi. Two angles of a triangle are 450 and 760. Calculate the size of its third angle.
ii. Draw ∆PQR and show P as x0. Q is twice as big as P and R = 510.
a. Make an equation in x
b. Solve the equation.
c. Find the three angles of the triangle.
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------31
HOMEWORK:
State the sizes of the lettered angles in the figure below. Give reasons.
700
x0
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------32
WEEK 8
DATE:
CLASS: YEAR 7
TOPIC: CONSTRUCTION OF TRIANGLES
LEARNING OBJECTIVES: By the end of the lesson, the students should be able to:
i. construct equilateral, isosceles and scalene triangles respectively.
CLASS ACTIVITY:
A. Construct a triangle ABC where AB = 5.8cm, BC = 7cm, AC = 8cm.
B. Construct a triangle XYZ in which YZ = 6cm, ZX = 5cm and XY = 4cm.
33
C. Construct an isosceles triangle PQR whose sides are PQ = 5cm, QR = 8cm, PR =
8cm.
D. Construct a triangle ABC, in which AB = 7cm, <A = 500 and <b = 750
34
E. Construct a triangle PQR, in which PQ = 6cm, <P = 60 0 and <q = 450
F. Construct a triangle ABC, in which AB = AC = BC = 8cm
35
HOMEWORK:
Construct the following triangles:
a. ∆ABC, in which AB = BC = 8cm and BC = 6cm
b. ∆ABC, in which <A = 600, <B = 900 and AB = 6cm
c. ∆ABC, in which AB = 5cm, <B = 800 and BC = 3cm.
36
WEEK 9
DATE:
CLASS: YEAR 7
TOPIC: PLANE SHAPES I
LEARNING OBJECTIVES: By the end of the lesson, the students should be able to:
i. state the meaning of plane shapes correctly.
ii. outline at least five examples of plane shapes.
iii. list at least three properties of some plane shapes
A. MEANING OF PLANE SHAPES:
Plane shapes are two-dimensional shapes bounded by lines known as sides. Any shape
drawn on a plane is called a two-dimensional shape (or 2-D shapes for short). When we
say a figure is two- dimensional, we mean it can be measured along x and y axes i.e. it
has length and width or breadth.
B. TYPES OF PLANE SHAPES:
Common plane shapes are:
1. Triangles
2. Quadrilaterals
3. Polygons
4. Circles
Triangles and quadrilaterals are examples of polygon. However, because triangles and
quadrilaterals have their own special properties they are usually dealt with separately.
We have dealt with Triangles in a previous lesson. We are now going to discuss the
quadrilaterals.
A quadrilateral is a four-sided plane shape with four angles.
Examples include:
i. Square
Properties:




It has all its sides equal
Each angle is 900
The opposite sides are parallel
It has four lines of symmetry
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ii. Rectangle
Properties:




Its opposite sides are equal and
Each angle is equal to 900.
The opposite sides are parrallel
It has two lines of symmetry
iii. Parallelogram:
Activity: Highlight four properties of a parallelogram
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------iv. Rhombus:
Draw a rhombus here!
Properties:
 It has all its four sides equal in length
 Opposite sides are parallel
 Opposite angles are equal
Any other property of the rhombus, not mentioned above, list them here!
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
38
v. Trapezium:
Activity: Outline four properties of trapezium.
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------HOMEWORK:
List any two other plane shapes not mentioned above. Draw any one of them and them
write out at least four properties of the shape drwan.
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------39
Polygon:
A polygon is any closed shape that has three or more straight sides. Thus, rectangles,
squares and triangles are all examples of polygons.
The table below shows some special polygons and their sides.
Names of Polygons
Number of sides
Triangle
3
Quadrilateral
4
Pentagon
5
Hexagon
6
Heptagon
7
Octagon
8
Nonagon
9
Decagon
10
Find out the special name for the polygon with the following sides:
a. 11 sides _________________________________________________________________________
b. 12 sides _________________________________________________________________________
There are two types of polygons. They are:
i. Regular Polygons
ii. Irregular Polygons
a. Irregular Polygons:
When the sides of a polygon and the included angles are not equal it is called an
irregular polygon. Examples are irregular pentagon and irregular hexagon shown
below.
Irregular Pentagon
Irregular Hexagon
40
b. Regular Polygon:
A polygon that has all its sides and angles equal is called a regular polygon. Examples
of regular polygons are: equilateral triangle, square, regular pentagon, hexagon, etc
Regular Hexagon
regular pentagon
CLASSWORK:
Differenciate between regular polygons and irregular polygons.
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Circles:
A circle is a plane shape that has set of points equidistant from a fixed point, O. The
fixed point is the centre of the circle as shown in the diagram below. A circle has
infinite lines of symmetry.
O
41
The parts of a circle include:
The circumference is the distance around the circle.
A radius (plural radii) is any straight line joining the centre of the circle to any point
on the circumference.
A chord is any straight line joining two points on the circumference.
A diameter is any chord that goes through the centre of the circle.
A sectoris the region between two radii and the circumference.
A semicircleis a sector between a diameter and the circumference, i.e. half a circle.
A segment is the region between a chord and the circumference.
CLASSWORK:
Draw a circle and include the following parts: two radii, a sector, a chord, a segment, a
diameter and an arc. Label each part and shade any regions.
42
HOMEWORK:
1. Write down the names of these shapes:
(i)
(ii)
(iii)
2. A polygon with seven sides is called.........................................................................
3. The simplest form of polygon is a.............................................................................
4. Which of the following quadrilaterals has only one pair of parallel sides? (a) Trapezium
(b) rhombus (c) parallelogram (d) square
5. A straight line joining two points on the circumference is called...................................
6. A regular polygon has all its sides ...................... and all its angles...........................
7. The distance around the circle is................................................................................
8. The number of sides of a polygon is not equal to the number of angles (True/False)
9. All the sides of an equilateral triangle are ................... and each angle is...................
10. A polygon with 13 sides is called …………………………………………………………………
43
WEEK 10
DATE:
CLASS: YEAR 7
TOPIC: PLANE SHAPES II
LEARNING OBJECTIVES: By the end of the lesson, the students should be able to:
i. state the meaning of perimeter and area.
ii. state the formula for the perimeter of a square.
iii. state the formula for the area of a square.
iv. solve problems on the perimeter and area of a square.
A. MEANING OF PERIMETER AND AREA
i. Perimeter:
The perimeter of a plane shape is the length of its outside boundary or the distance
around its edges.
The unit of measurement of Perimeter:
Perimeter is measured in length units. These are kilometres (km), metres (m),
centimetres (cm) and millimetres (mm).
ii. Area:
The area of a plane shape is a measure of the amount of surface it covers or occupies.
Area is measured in square units, e.g. square metre (m2), square millimetres (mm2), etc.
B. PERIMETER OF A SQUARE:
A square is a regular four sides shape. If the length of one side of a square is l, then,
Perimeter of square = l x 4 = 4l
As perimeter of square = 4l,
Length of side of square =
Examples:
1. Calculate the perimeter of a square of side 12.3cm.
Solution:
Perimeter = 12.3 x 4
Perimeter = 49.2cm.
44
CLASSWORK:
1. A square assembly area has a perimeter of 58cm. Find the length of the side
of the assembly area.
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------2. The table below gives details about some squares. Complete the table.
a.
b.
c.
d.
e.
Length
8cm
9.3m
Perimeter
60cm
11m
250m
850mm
HOMEWORK:
A square football pitch measures 80m in length. In a training session, the coach
tells the team to run ten times round the pitch. How far do they run?
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------45
C. AREA OF A SQUARE:
A square is a rectangle whose length and breadth are equal, thus:
Area of square = (length of side) 2
Therefore,
Length of side =
𝑎𝑟𝑒𝑎 𝑜𝑓 𝑠𝑞𝑢𝑎𝑟𝑒
Examples:
1. Calculate the area of a square advertising board of length 5 m.
Solution:
Area of square board = 5 m x 5 m = 25m 2
CLASSWORK:
1. The area of a square plot is 144m2. Calculate the length of a side of the plot.
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------2. If the width of a rectangle is equal to the length of a square and the rectangle
measures 6 cm by 4 cm. Find the area of the square.
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------3. The table below gives details about some squares. Complete the table.
a.
b.
Length of side
14cm
Area
400m2
46
HOMEWORK:
Calculate the area of the figures given below:
13cm
10cm
5mm
9.5cm
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------47