Construction of Parallel and Perpendicular lines

Subject : MATHEMATICS

Class : JSS 1

Term :THIRD TERM

Week : WEEK EIGHT

Reference Materials

• Scheme of Work
• Online Information
• Textbooks
• Workbooks
• 9 Year Basic Education Curriculum

Previous Knowledge :

The pupils have previous knowledge of

Angles: Identification and properties of angles

Behavioural Objectives :  At the end of the lesson, the pupils should be able to

• construct parallel lines and perpendicular lines
• bisect a given line of segment
• construct angles like sixty degrees , ninety degrees etc

WEEK EIGHT

TOPIC: 

CONSTRUCTION OF PARALLEL LINES USING RULER AND SET SQUARE ONLY

CONTENT

1. To draw parallel lines (Horizontally) using a ruler and set-square only.
2. To draw parallel lines (Non-horizontal) using a ruler and set-square only.

      iii. Application of construction. Plane figure.

1. Drawing parallel lines (Horizontally using a ruler and set-square only.

     (a) Guidelines for constructions.

In geometry, to construct a figure means to draw it accurately. Accurately construction depends on using measuring instruments properly.

Generally, to carry out a construction, you require a sharp pencil, compasses, protractor and a good ruler, set-square and dividers are also necessary.

When making constructions, the following guidelines should be followed.

(1) A short pencil of about 6cm should be fixed on the fixed on the pair of compasses when constructing to avoid any obstruction when turning your compass round to draw arcs.

(2) Ensure that the pivot of your pair of compasses is tight to avoid unwanted shift when carrying out your construction.

(3) To ensure that your lines and points are as fine and accurate as possible make use of a hard pencil with a sharp point.

(4) Before making the actual construction, make a rough sketch of the problem under consideration. This will make the construction of the actual problem easy.

(5) Leave all your arcs and construction lines visible. Do not clean any arc that leads you to your final result.

(6) Double lines and arcs in constructions are not allowed, hence clean up all double arcs and lines neatly and re-draw.

(b) To draw parallel lines

(i) Definition:  Parallel lines are lines that do not meet. They always have the same distance apart and are in the same direction.

(ii) Example

Draw accurately a line through 0, parallel to line MN.

Solution

Using a ruler and –square (i) Place one edge of the set-square along the given line MN. (ii) Place a ruler along one of the other edges of the set-square as shown in the diagram below.

(iii) Hold the ruler firmly with one hand and then slide the set- square with the second along the edge of the ruler until you reach point O.

(iv) Draw the line with a sharp pencil

Use a ruler and set square to draw four lines that are parallel to each other.

 (ii) To draw parallel lines (Non- horizontal) using a ruler and set square.

Example 

Draw a line through point O, Parallel to line MN.

Solution

The set square and ruler are placed accordingly as shown in the diagram.

EVALUATION QUESTION

(i) Use ruler and Set Square to construct a pair of parallel lines that are 3cm apart.

(ii) Draw accurately a line through C parallel to AB in this diagram using ruler and set square.

CONSTRUCTION OF PERPENDICULAR LINE USING RULER AND SET SQUARE ONLY

Definition

(a) TYPES OF LINES

(i) POINT: A point is used to denote a position of an object in space and it has a negligible size or magnitude. It is usually represented by a dot (.) or a cross (x)

(ii) A LINE: A line is made up a set of points. The arrows at both ends show that line Mn continues forever on both directions.

(iii) STRAIGHT LINE: A straight line is the shortest distance two 

points such as points m and n 

(iv) HORIZONTAL LINE: A line drawn straight across the page is called a horizontal line 

(v) VERTICAL LINE: A line drawn straight up or down a page is called a vertical line.

(vi) ANGLES: When two lines meet at a point, an angle is formed. Angle are measured in degrees. The symbol for degrees is O. Therefore an angle may be describe as a measure of the degree of rotation between two lines that intersect a point. For example in the diagram below the point where lines AO and BO meet is O. the angle formed is θ (theta).

AO and BO are called the arms of the angle θ and point O is called the vertex.

(vii) PERPENDICULAR LINES: When a horizontal line meets (intersects) a vertical line, both lines are said to be perpendicular to each other.

The symbol for perpendicular lines is        i.e. AO      BO

That is: Two lines are perpendicular to each other if they intersect at right angles (i.e. 900) example: 

PQ      RQi.e. line PQ is perpendicular to line RQ 

AB      XY

Line AB is perpendicular

to line XY.

Presentation

The topic is presented step by step

Step 1:

The class teacher revises the previous topics

Step 2.

He introduces the new topic

Step 3:

The class teacher allows the pupils to give their own examples and he corrects them when the needs arise

EVALUATION 

Evaluation question

Give a brief definition and a sketch diagram to explain them.

(a) a straight line (b) perpendicular line

II CONSTRUCTION OF PERPENDICULAR LINES EXPLANATION

To construct a perpendicular from a point to a line using ruler and set square.

(1) Place a ruler along the lines.

(2) Use the two edges of a set square which are the arms of its right angle. Place one of these edges along the ruler. Slide the set square along the ruler until the other edge reaches P.

(3) Hold the set square firm. Draw the line through P to meet the line perpendicularly.

Example

Draw a perpendicular line to PQ at R

Solution

(i) Place one edge of the right angle of the set square along the given line (i.e. PQ)

(ii) Place a ruler along the hypotenuse as show below.

(iii) Hold the ruler firmly with one hand and then slide the set square with the second hand along the edge of the ruler until the required position R is reached as shown in the diagram below. Draw a line through R.

Evaluation Question

From This pentagon, draw perpendicular line from P to 

the five sides using ruler and set square.

(iii) APPLICATION OF CONSTRUCTIONS: DRAWING

PLANE FIGURE E.G. (RECTANGLE)

Example:

Draw accurately a rectangle of length 8cm and width 5cm using ruler and set square.

Solution

EVALUATION QUESTION

Use ruler set square and protractor construct parallelogram ABCD with AB = 8cm and BC = 5cm and ABC = 1200.

GENERAL EVALUATION

1. use ruler and set square  to construct a pair of parallel lines that are 5cm apart 
2. Draw accurately a line through D parallel to BC in this diagram using ruler and set square.

WEEKEND ASSIGNMENT 

1. In construction, __________ is an instrument for drawing lines and measurement of length. (a) compass (b) dividers (c) ruler (d) protractor
2. The angles between two lines that are perpendicular is (a) 700 (b) 900 (c) 800 (d) 1000
3. In construction __________ is an instrument for constructing  and measuring angles (a) set square (b) compass (c) protractor (d) ruler
4. These instruments are necessary for construction except _________ (a) compass (b) ruler (c) block (d) protractor 
5. In construction you must be __________ (a) careful (b) careless (c) untidy (d) unprepared 

THEORY 

1. In construction, name five basic instruments that are very important 
2. Use ruler and set square construct a rectangle of length 6cm by 3cm.

Conclusion :

The class teacher wraps up or conclude the lesson by giving out short note to summarize the topic that he or she has just taught.

The class teacher also goes round to make sure that the notes are well copied or well written by the pupils.

He or she does the necessary corrections when and where  the needs arise.

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