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VEA
Bringing Learning to Life
Program Support Notes
Middle Secondary
23mins
Mathemania 3 Series
Naming and
Measuring Angles
Steve Wright, B.Sc. Dip.Ed.,
Dip.Comp., Cert. IV Work Place Assessor
Teacher Notes by
Produced by VEA Pty Ltd
Commissioning Editor Christine
Henderson B.Sc.
Ph.D. Dip.Ed.
McAuliffe Dip.Art (Film &
TV) Dip.Ed. B.Ed. Ph.D.
Executive Producer Mark
© VEA Pty. Ltd.
Suitable for:
Maths
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These notes can be freely copied for
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Naming and Measuring Angles - Mathemania 3 Series
For Teachers:
Brief Summary of Program
This program illustrates the mathematical ideas associated with angles using examples from the world
around us.
Measuring rotation using a protractor is clearly demonstrated for acute and obtuse angles.
Relationships between the angles formed by a transversal cutting a pair of parallel lines are explored
using clear on-screen graphics and simple demonstrations. Conditions for congruent triangles are
illustrated using clear informal methods. Accurate use of mathematical symbols is used throughout.
DVD Timeline
00:00:00
00:00:22
00:02:49
00:03:23
00:08:51
00:09:19
00:13:23
00:14:01
00:17:44
00:18:33
00:21:36
00:21:56
00:22:06
00:22:37
Introduction
Looking at angles
Summary
Naming and measuring angles
Summary
Angle relationships
Summary
Congruent triangles part 1
Summary
Congruent triangles part 2
Summary
Conclusion
End credits
Program end
Other Relevant Programs Available from VEA
Similarity, Ratio and Proportion
Geometric Transformations
Geometric Constructions
Triangles and Quadrilaterals
Coordinate Geometry
Please visit our website for many more relevant programs www.vea.com.au
VEA – Bringing Learning to Life
2
Naming and Measuring Angles - Mathemania 3 Series
Student Worksheet:
Before Viewing the Program
1.
Look around your classroom. What angles can you see? List at least 10. Group the angles that are
about the same size. Where do you most commonly see right angles in the classroom?
_______________________________________________________________________________
_______________________________________________________________________________
_______________________________________________________________________________
_______________________________________________________________________________
_______________________________________________________________________________
2.
Do you know what tools builders use to set and transfer angles?
_______________________________________________________________________________
_______________________________________________________________________________
3.
Find all the factors of the numbers 10 and 60. From these results can you suggest why an hour is
divided into 60 minutes rather than 10?
_______________________________________________________________________________
_______________________________________________________________________________
_______________________________________________________________________________
_______________________________________________________________________________
3
Naming and Measuring Angles - Mathemania 3 Series
While Viewing the Program
1.
An angle consists of two rays which start from the same point. What is this point called?
_______________________________________________________________________________
_______________________________________________________________________________
2.
Complete the following table.
Description
Symbol
Ray from A through B
AB
Line through A and B
Line segment AB
3.
What instrument is used to measure angles?
_______________________________________________________________________________
4.
How many degrees are in one revolution?
_______________________________________________________________________________
5.
How many degrees in a quarter of a revolution?
_______________________________________________________________________________
6.
How do we describe the angle between a horizontal and vertical plane?
_______________________________________________________________________________
4
Naming and Measuring Angles - Mathemania 3 Series
7.
Complete the following table.
Angle Name
Angle Size
900
1800
3600
0<A<90
Obtuse
8.
90<A<180
Complete the following from the program
Angle Name
Angle Type
5
Approximate Size
Naming and Measuring Angles - Mathemania 3 Series
9.
List the corresponding angles in this diagram.
1
3
5
2
4
6
7
8
_______________________________________________________________________________
_______________________________________________________________________________
10. List the pairs of alternate angles in this diagram.
1
3
2
4
_______________________________________________________________________________
_______________________________________________________________________________
11. Co-interior, C angles, A and B are supplementary. A + B =
?
_______________________________________________________________________________
_______________________________________________________________________________
6
Naming and Measuring Angles - Mathemania 3 Series
12. QUIZ
1350
?
?
760
13. What is the maximum sized angle that can be measured directly using a protractor?
_______________________________________________________________________________
14. Which point is the vertex in the following angles?
∠ABC , ∠HJK
_______________________________________________________________________________
15. What does congruent mean?
_______________________________________________________________________________
_______________________________________________________________________________
16. What is a pair of triangles called if they have the same size and shape?
_______________________________________________________________________________
17. Complete the following table for conditions of congruence.
Condition
Description
SSS
SAS
Two congruent sides and included angle
ASA
7
Naming and Measuring Angles - Mathemania 3 Series
After Viewing the Program
1.
How could you fold paper to construct the following sized angles?
(a) 900
2.
(b) 450
(d) 1350
(e) 2700
Find the angle between the hour and minute hands of a clock at the following times.
(a) 9 am.
(b) 10 am.
(e) 12.15 am. (f) 6.30pm.
3.
(c) 22.50
(c) 5 am.
(d) 12 am.
(g) 1.15 pm.
(h) 12.05 pm.
Research the Babylonian’s base 60 number system. Find out some of the accomplishments of this
civilization which required accurate measurement.
8
Naming and Measuring Angles - Mathemania 3 Series
Suggested Student Responses:
While Viewing the Program
1.
An angle consists of two rays which start from the same point. What is this point called?
Vertex
2.
Complete the following table.
Description
Symbol
Ray from A through B
AB
Line through A and B
AB
Line segment AB
AB
3.
What instrument is used to measure angles?
Protractor
4.
How many degrees are in one revolution?
3600
5.
How many degrees in a quarter of a revolution?
3600/4 = 900
6.
How do we describe the angle between a horizontal and vertical plane?
A right angle
7.
Complete the following table:
Angle Name
Angle Size
900
1800
3600
0<A<90
90<A<180
right
straight
revolution
acute
Obtuse
8.
Complete the following from the program:
Angle Name
∠KLM
∠EFG
∠XYZ
Angle Type
Approximate Size
450
1400
900
Acute
Obtuse
Right
9
Naming and Measuring Angles - Mathemania 3 Series
9.
List the corresponding angles in this diagram.
1
3
5
2
4
3
6
5
4
6
7
8
10. List the pairs of alternate angles in this diagram.
1
4
2
3
1
3
2
4
11. Co-interior, C angles, A and B are supplementary. A + B = 1800
12. QUIZ
1350
1040
450
760
10
8
7
2
1
Naming and Measuring Angles - Mathemania 3 Series
13. What is the maximum sized angle that can be measured directly using a protractor?
1800
14. Which point is the vertex in the following angles?
B and J
∠ABC , ∠HJK
15. What does congruent mean?
Equal
16. What is a pair of triangles called if they have the same size and shape?
Congruent
17. Complete the following table for conditions of congruence.
Condition
Description
SSS
Three sets of congruent sides
SAS
Two congruent sides and included angle
ASA
Two sets of congruent angles and the included side
11