1. Angles
Stage 4

2. Angles In this topic the following concepts are covered:
The language and notation of angles
Angles at a point and adjacent angles
Complementary and supplementary angle relationships
Corresponding, alternate and cointerior angle relationships
Parallel and perpendicular lines
Applications of angle relationships

3. Angles - Vocabulary
angle measure acute obtuse arms degrees protractor point straight revolution parallel vertex
perpendicular right reflex complementary adjacent interval
vertically opposite ruler supplementary length ray proof
transversal cointerior alternate
corresponding reasoning properties
lines equal proof
conventions condition geometry
unknown common arm
diagrams geometric

5. Use the list words below to fill in the blanks in this passage:
A line goes on forever. If it has one endpoint it is called a _______. If it has two endpoints it is called an _______. We can _______ the _________ of an interval using a _______. When two lines meet an _________ is formed. The point of an angle is called a _________. To measure the size of an angle, a __________ is used. Two lines which are always the same distance apart and never meet are called ________. Two lines which meet at a right angle are called __________. You can check whether two lines are perpendicular by using a ____ _______.

6. Measuring Angles We use a protractor to measure angles.
Move the protractor so that the highlighted area matches with the vertex of the angle.
Read around the curve of the protractor, making sure your answer makes sense!

7. Use the protractor to measure these angles.

8. Use a ruler and a protractor to accurately draw each of the
following angles:
650 e) 800
1200 f) 240
c) g) 1600
480 h) 900
Using two joined straws, make an estimate of each of the angles
above, working in pairs. Test to see how close your estimates are!
Signpost p 120 Q 1-13

9. Copy the diagram, matching the pairs correctly.
Then write a definition of each type of angle next to the diagram.
Signpost p 126 Q 1-8

10. Definitions:
In groups, come up with the best possible definition for each of the following geometry terms, including a diagram:
Line –
Ray –
Line interval –
Concurrent lines –
Collinear points –
Parallel lines –
Perpendicular lines -

11. Labelling Angles
We can name an angle by using a point on each ray and the vertex.
The angle below can be named as angle ABC or as angle CBA or as <ABC or as <CBA.
Do you see how the vertex point is always given in the middle.
How could you label this angle?

14. Adjacent Angles Adjacent angles must have: • a common vertex
• a common arm and
• lie on opposite sides of the common arm.
For example, ∠ABC and ∠CBD are adjacent.
• B is the common vertex.
• BC is the common arm.
• ∠ABC and ∠CBD lie on opposite sides of BC.

17. Challenge: How many different ways can you label this angle?

19. 6(b)

23. Angles at a point:
It stands to reason that if the angles lying on one straight line add
up to 1800, put two straight lines together, the angles will add to 3600.
In fact, angles at a point ALWAYS add to 3600, whether the lines are
straight or not.

24. Vertically Opposite Angles
In the diagram below, what is the size of the indicated angle?
How do you know that WITHOUT measuring the other angles
in the diagram?

27. Signpost p 130 Q 1-15

31. Corresponding, Alternate and Cointerior Angle Relationships
There are three new angle relationships you will need to recognise
and use:
These become more useful when combined with parallel lines.

34. When a transversal cuts parallel lines, then:
Corresponding angles are always equal:
Example:
Alternate angles are always equal:
Example:
Co-Interior angles always add to give 1800
(They are supplementary angles):
Example:

47. Checking whether lines are parallel: