TOPIC 4: SHAPES AND FIGURES – MATHEMATICS NOTES STANDARD THREE
Basic figures which are used in constructing various geometrical figures.
- Point
- Line
- line segment
- a ray
A point
A point is a geometrical figure which represents location of a place.
- A point has no size and it is shown by a dot.
- It has no length and width.
- Points are represented by capital letters. The following are examples of points.
The points A, B, and C in the examples represent different location of places.
A line
A line is made of a set of points joined together, and extends on opposite sides infinitely.
- A line is often indicated by a symbol ↔ to show the infinite nature.
- A straight line can be denoted by any two distict points on the line.
Examples of straight lines.
Therefore, represents a straight-line EF or FE, respectively.
Similarly, are straight lines.
Example 1
Draw a line which is longer than 10 cm from point A to point B.
Solution
A line drawn is longer than 10 cm from point A to B.
Line segment
A line segment is a straight line that is constructed by joining two distinct points.
The length of a line segment can be determined because it has end points. A line segment whose end points are A and B is denoted by AB or BA or line segment AB or line segment BA.
Activity 2: Drawing a line segment
1. Connect points A and B, C and D, and E, and F, using a pencil and free hand.
2. Connect points A and B, C and D, and E and F using a pencil and ruler.
3. What did you observe in task 1 and 2?
4. In which task, the following lines were constructed?
Features of a line segment:
A line segment has the following features:
- It is straight.
- It has no thickness.
- It has two endpoints.
Example 1
In each of the following diagrams, find out if it is a line segment, a line or not.
Answer
- Is a line because it has no end points.
- Is a line segment because it has two end points.
- Is neither a line nor a line segment because it has one point and an arrow on the other end.
Example 2
Write the name of each of the following line segments:
Answer
Example 3
Write the names of all possible line segments in the following figure:
Answer
Example 4
How many line segments are there in the following figure?
Answer
There are eight line segments.
Exercise 1
1. Draw line segments of the following lengths:
PQ = 4 cm ___
CD = 5 cm ___
LM = 6 cm
JK = 7 cm
XY = 8 cm
EF = 9 cm
MN =10 cm
2. Which of the following represents a line segment?
How many line segments does a square have?
3. What is the difference between a line segment and a line?
4. What are the examples of line segments in real life?
A ray
A ray is a line with a fixed starting point but has no end point.
A ray is formed when a line segment is drawn and extended at one of its end points and marked with an arrow.
Examples of rays are as shown in the following diagram:
A ray is represented by the symbol → on the top of its notation. For example, the ray AB is written as 
, and the ray BA is written as 
Activity 3: Drawing a ray
- Use a ruler to draw a line segment AB.
- Extend the line at any point and put an arrow-head to show the direction.
- Repeat tasks 1 and 2 to draw three more rays and name them.
Example 1
What is the endpoint of a ray AC?
Answer
Since the point of origin of a ray is also called its endpoint. Therefore, the end point of the ray AC is point A.
Example 2
Which rays are opposite to each other in the following figure?
Answer
Ray AB and ray AE are opposite rays in the given figure. The rays start from point A and proceed in the opposite direction to form a straightline EB.
Example 3
Write the names of all rays formed from the following figure:
Answer
From the given figure, the rays are:
Activity 4: Drawing a straight line
- Use a ruler to draw two rays, one pointing towards the left and the other towards the right.
- Connect the initial points of the two rays in task 1 to get a straight line.
Exercise 2
1. Draw and label two line segments.
2. Draw and label three straight lines.
3. State the diference between a straight line and a line segment.
4. Can you draw a 4 cm line segment without a ruler? Give reasons.
5. Draw rays XY and YX.
6. Give the difference between a line segment and a ray.
7. Which instrument can be used to measure a line segment of length 5 cm?
8. Determine the number of line segments in the following line.
9. Draw a line segment PQ and state the name of the end points.
10. Join three line segments AB, BC, and CA. Then, state the name of the figure formed.
11. How many rays can you draw from a single point?
12. Give at least three examples that can be considered to represent a ray in our daily life.
CONSTRUCTING PLANE FIGURES
A plane figure is a two-dimensional figure. which has only length and width.
It has no thickness or depth.
All plane figures have flat shapes and exist on flat surfaces.
Types of plane figures
- Squares
- Rectangles
- Triangles
- Circles
- Ovals
ACTIVITY 5: CONSTRUCTING PLANE FIGURES USING POINTS
1. Study the following points
(a) Use a pencil and a ruler to connect points A and B, C and D, A and D, and D and C.
(b) Measure and record the lengths of line segments AB, AD, CD and BC.
(c) Name the plane figure formed in task 2.
(d) How many line segments are there in a triangle?
(e) Connect the points E, F, G, and H to form the following plane figures:
- Two triangles.
- Four triangles.
1. How many line segments does a kite have?
2. How many line segments are in the following figure?
Names of plane figures
Plane figures are named according to:
- Shapes
- angles
- sides
The following are examples of plane figures and their names:
A square and a rectangle are plane figures which have four sides each. Their difference is that all the sides of the square have equal length, while in a rectangle, only the pairs of opposite sides have equal lengths.
Activity 6: Drawing plane figures by using ICT
- Identify a computer programme for drawing plane figures.
- Use the programme in task 1 to draw squares, triangles, circles, and rectangles of different sizes.
- Draw five plane figures with at least five sides, and name them.
- Draw more plane figures to enhance your competence.
Example
Answer
(a) There are 8 sides; it is an octagon.
(b) There are 4 sides; it is a rectangle (or quadrateral).
(c) There are 3 sides; it is a triangle.
(d) It is a circle.
Exercise 4
1. Carefully study the plane figures a to j and answer thequestions that follow:
(a) Draw all the figures with four sides.
(b) How many figures are triangles?
(c) Write down the letters labelled in the circles.
(D) Make the figures identified with letters labelled a,b, d, e, and f by cutting a piece of paper or manila card.
2. The following diagram shows a house made of plane figures. Draw all the plane figures found in the diagram:
Activity 7: Recognising plane figures by using ICT
Use online programmes to identify different types of plane figures and match them with real objects.
Summary
- Two dimensional figures are such as squares, rectangles, triangles, and hexagons.
- A square has sides which are equal in length, while a rectangle has pairs of opposite sides with equal length.
- A line segment is drawn by joining two points.
- A ray has an initial point and extends one side infinitely.
REVISION EXERCISE
1. Draw and label two-line segments of length 4 cm and 5 cm, respectively.
2. Draw a ray PQ.
3. How many ends does a ray have?
4. Write the names of the rays found in the following figure.
5. How many straight lines does the following figure have?
6. Write down the names of the straight lines found in the following figure.
7. How many angles do the following figures have?
(a) Triangle
(b) Pentagon
(c) Hexagons
8. Draw any two plane figures.
9. Which of the following figures are not rectangular? Give reasons for your answer
10. How many triangles are there in the following figure?
11. Study the following diagram, and then answer the questions that follow:
12. How many line segments are in the figure?
13. Name all plane figures found in the diagram.
14. Use the following figure to answer the questions that follows:
(a) Name all points.
(b) Name all the line segments.
(c) Name all the rays.
(d) Name a straight line in three ways.
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