1. G1 Parallel and perpendicular lines
Boardworks KS3 Maths 2009
G1 Parallel and perpendicular lines
G1 Parallel and perpendicular lines
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For more detailed instructions, see the Getting Started presentation.

2. G1.1 Labelling lines and angles
Boardworks KS3 Maths 2009
G1 Parallel and perpendicular lines
G1.1 Labelling lines and angles

3. Boardworks KS3 Maths 2009 G1 Parallel and perpendicular lines
In Mathematics, a straight line is defined as having infinite length and no width.
A line is the shortest distance between two points. Mathematically, a line only has one dimension, length and no width.
We cannot draw a line like this in real life because it would be invisible.
The two arrows at either end indicate that the line is infinite.
Is this possible in real life?

4. Labelling line segments
Boardworks KS3 Maths 2009
G1 Parallel and perpendicular lines
Labelling line segments
When a line has end points we say that it has finite length.
It is called a line segment.
We usually label the end points with capital letters.
The line segment shown below has end points A and B. A B
We can call this line ‘line segment AB’.

5. Boardworks KS3 Maths 2009 G1 Parallel and perpendicular lines
Labelling angles
When two lines meet at a point an angle is formed. A B C
An angle is a measure of the rotation of one of the line segments relative to the other.
Pupils often find the naming of angles difficult, particularly when there is more than one angle at a point.
At Key Stage 3 this confusion is often avoided by using single lower case letters to name angles.
We label points using capital letters.
The angle can then be described as ABC
or ABC
or B.
Sometimes instead an angle is labelled with a lower case letter.

6. Conventions, definitions and derived properties
Boardworks KS3 Maths 2009
G1 Parallel and perpendicular lines
Conventions, definitions and derived properties
A convention is an agreed way of describing a situation.
For example, we use dashes on lines to show that they are the same length.
A definition is a minimum set of conditions needed to describe something.
60°
The statement that an equilateral triangle has three equal sides and three equal angles is a definition.
Discuss the difference between a convention, a definition and a derived property.
60°
60°
A derived property follows from a definition.
For example, the angles in an equilateral triangle are each 60°.

7. Convention, definition or derived property?
Boardworks KS3 Maths 2009
G1 Parallel and perpendicular lines
Convention, definition or derived property?
Decide whether the information given is a convention, a definition or a derived property.

8. G1.2 Parallel and perpendicular lines
Boardworks KS3 Maths 2009
G1 Parallel and perpendicular lines
G1.2 Parallel and perpendicular lines

9. Boardworks KS3 Maths 2009 G1 Parallel and perpendicular lines
Spot the lines!
Use this slide to introduce the idea of parallel and perpendicular lines. Ask students if they know what these are, and then ask them to point out examples in the cartoon. Ask students to estimate the angle between the fallen skier’s skis. Are they perpendicular?

10. Boardworks KS3 Maths 2009 G1 Parallel and perpendicular lines
Lines in a plane
What can you say about these pairs of lines?
When we discuss lines in geometry, they are assumed to be infinitely long. That means that any two lines in the same plane (that is in the same flat two-dimensional surface) will either intersect at some point or be parallel. This needs to be remembered in the discussion of the pair of parallel lines here. To be parallel, the lines must not intersect no matter how far they are extended.
These lines cross, or intersect.
These lines do not intersect.
They are parallel.

11. Boardworks KS3 Maths 2009 G1 Parallel and perpendicular lines
Lines in a plane
A flat two-dimensional surface is called a plane.
Any two straight lines in a plane either intersect once …
This is called the point of intersection.

12. Boardworks KS3 Maths 2009 G1 Parallel and perpendicular lines
Lines in a plane
… or they are parallel.
We use arrow heads to show that lines are parallel.
Parallel lines will never meet.
They stay an equal distance apart.
Pupils should be able to identify parallel and perpendicular lines in 2-D and 3-D shapes and in the environment.
For example: rail tracks, double yellow lines, door frame or ruled lines on a page.
We can say that parallel lines are always equidistant.
Where do you see parallel lines in everyday life?

13. Boardworks KS3 Maths 2009 G1 Parallel and perpendicular lines
What is special about the angles at the point of intersection here?
a = b = c = d a b d
Each angle is 90. We show this with a small square in each corner. c
Pupils should be able to explain that perpendicular lines intersect at right angles.
Lines that intersect at right angles are called perpendicular lines.

14. Parallel or perpendicular?
Boardworks KS3 Maths 2009
G1 Parallel and perpendicular lines
Parallel or perpendicular?
Use this activity the identify whether the pairs of lines given are parallel or perpendicular.
This activity will also practise the labeling of lines using their end points.

15. The distance from a point to a line
Boardworks KS3 Maths 2009
G1 Parallel and perpendicular lines
The distance from a point to a line
What is the shortest distance from a point to a line? O
Ask pupils to point out which line they think is the shortest and ask them what they notice about it.
Ask pupils if they think that the shortest line from a point to another line will always be at right angles.
Reveal the rule.
The shortest distance from a point to a line is always the perpendicular distance.

16. Drawing perpendicular lines with a set square
Boardworks KS3 Maths 2009
G1 Parallel and perpendicular lines
Drawing perpendicular lines with a set square
We can draw perpendicular lines using a ruler and a set square.
Draw a straight line using a ruler.
Place the set square on the ruler and use the right angle to draw a line perpendicular to this line.

17. Drawing parallel lines with a set square
Boardworks KS3 Maths 2009
G1 Parallel and perpendicular lines
Drawing parallel lines with a set square
We can also draw parallel lines using a ruler and a set square.
Place the set square on the ruler and use it to draw a straight line perpendicular to the ruler’s edge.
Slide the set square along the ruler to draw a line parallel to the first.