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MA4-18MG Angle Relationships
Summary of substrands
Duration
2 weeks
MA3-16MG measures and constructs angles, and applies angle relationships to find unknown angles.
Stage 3 - Angles 1
Estimate, measure and compare angles using degrees (ACMMG112)
Construct angles using a protractor (ACMMG112)
Stage 3 - Angles 2
Investigate, with and without the use of digital technologies, angles on a straight line, angles at a point, and vertically opposite angles; use the results to find
unknown angles (ACMMG141)
Unit overview
The development of knowledge and understanding
of angle relationships, including the associated
terminology, notation and conventions, is of
fundamental importance in developing an
appropriate level of knowledge, skills and
understanding in geometry. Angle relationships
and their application play an integral role in
students learning to analyse geometry problems
and developing geometric and deductive reasoning
skills, as well as problem-solving skills.
Angle relationships are key to the geometry that is
important in the work of architects, engineers,
designers, builders, physicists, land surveyors, etc,
Outcomes

MA41WM communicates and connects
mathematical ideas using appropriate
terminology, diagrams and symbols
 MA42WM applies appropriate
mathematical techniques to solve
problems
 MA43WM recognises and explains
mathematical relationships using
reasoning
MA418MG identifies and uses angle
relationships, including those related to
transversals on sets of parallel lines
Big Ideas/Guiding Questions
How do you know when two lines are parallel?
Students can measure the angle of various ramps, such as wheelchair
access ramps and skateboard ramps. For example, if given that a
wheelchair ramp must have a slope of 1 in 8, they could draw this and
discover what angle it has to be.
Could use the idea of the billiards table or a soccer goal to discover the
as well as the geometry that is common and
important in everyday situations, such as in nature,
sports, buildings, astronomy,art, etc.
angle that the ball needs to be hit or kicked on.
Key words
angle, obtuse, corresponding, reflex, co interior, degree, adjacent,
diagonal, parallel, revolution, complementary, straight, supplementary,
right-angled, perpendicular, vertically, opposite, protractor,
transversal, equilateral, acute, alternate, interior, exterior, interval,
complement, supplement,
Students in Stage 4 should write geometrical reasons without
the use of abbreviations to assist them in learning new
terminology, and in understanding and retaining geometrical
concepts, eg 'When a transversal cuts parallel lines, the cointerior angles formed are supplementary'.
In Stage 4, students should use full sentences to describe the
properties of plane shapes, eg 'The diagonals of a
parallelogram bisect each other'. Students may not realise that
in this context, the word 'the' implies 'all' and so this should be
made explicit. Using the full name of the quadrilateral when
describing its properties should assist students in remembering
the geometrical properties of each particular shape.
Students in Stage 4 should write geometrical reasons without
the use of abbreviations to assist them in learning new
terminology, and in understanding and retaining geometrical
concepts.
Catholic Perspectives
School
Free
Design
God has created the universe. A place of beauty and wonder.
Since the beginning of time, man has pondered about the universe and the stars. It is the use of geometry that has helped develop a deeper understanding
of our world.
The importance of Euclidean Geometry is one of historical and practical use for the study of mathematics in today’s society. Euclidean Geometry is one
of the oldest branches of mathematics, developed by Euclid in 300BC, and serves as a basis of modern mathematics that governs our world.
(www.muchmoremath.com/geometry)
Assessment Overview
Generally, teachers should design specific assessment tasks that can be drawn from a variety of the following sources of information and assessment strategies:
• student responses to questions, including open ended questions,
• student explanation and demonstration to others,
• questions posed by students,
• samples of student work,
• student produced overviews or summaries of topics,
• investigations or projects,
• students oral and written report
• practical tasks and assignments,
• short quizzes
• pen and paper tests, including multiple choice, short answer questions and questions requiring longer responses, including interdependent questions ( where one answer
depends on the answer obtained in the preceding part)
• open book tests
• comprehension and interpretation exercise
• student produced worked samples,
• teacher/student discussion or interviews
• observation of students during learning activities including the student’s correct use of terminology
• observation of a student participating in a group activity
References can be made to the relevant end of chapter review or screening tests found in textbooks or other resource areas


Content
Teaching, learning and
assessment
Use the language, notation and
conventions of geometry
Open discussion on ‘what is an angle’ ‘where
can you find angles’, ‘how do you measure
angles’
define, label and name points, lines
and intervals using capital letters
label the vertex and arms of
an angle with capital letters

Interactive protractor on Smart board
Look for angles in the environment or in
pictures from magazines and newspapers.
Group activity: Student to construct and label
the vertex and arms of a number of angles for
the other student to measure and name the
angle.
FREEFALL WORKSHEETS
GEOGEBRA
label and name angles using
or

Resources
notation
use the common conventions to
indicate right angles and equal
angles on diagrams
Practical activity: Give a page of different size
angles. Students to estimate the size of each
angle then measure the angle recording their
findings in a table. Could also include columns
to name the angle and identify the type of angle.
MATHLETICS ACTIVITIES:
Ruler and Protractors
Recognise the geometrical properties
of angles at a point

use the terms 'complementary' and
'supplementary' for angles adding to
90° and 180°, respectively, and the
associated terms 'complement' and
Some students may find the use of the terms
'complementary' and 'supplementary'
(adjectives) and 'complement' and 'supplement'
(nouns) difficult. Teachers should model the use
of these terms in sentences, both verbally and in
written form, eg, '50° and 40° are
complementary angles', 'The complement of 50°
is 40°'.
Useful websites for worksheets, interactive games, maths charts, flashcards
http://resources.woodlands-junior.kent.sch.uk/maths/units120.html
http://www.topmarks.co.uk/Interactive.aspx?cat=22
http://www.helpingwithmath.com/
'supplement'


use the term 'adjacent angles' to
describe a pair of angles with a
common arm and a common vertex
identify and name right angles,
straight angles, angles of complete
revolution and vertically opposite
angles embedded in diagrams
recognise that adjacent angles can
form right angles, straight angles and
angles of revolution (Communicating,
http://www.sheppardsoftware.com/math.htm
Students should be aware that
complementary and supplementary angles
may or may not be adjacent.
Students are to be encouraged to give reasons
when finding unknown angles.
For some students formal setting out could be
introduced.
For example, ABQ = 70º (corresponding
angles, AC PR)
www.au.ixl.com
Reasoning)
Sector graphs could be used to demonstrate
angles at a point.
Identify corresponding, alternate
and co-interior angles when two
straight lines are crossed by a
transversal (ACMMG163)

identify and name perpendicular
lines using the symbol for 'is
perpendicular to' (


The other two results then follow using
vertically opposite angles and angles on a
straight line. Alternatively, the equality of the
alternate angles can be seen by rotation about
the midpoint of the transversal
use the common conventions to
indicate parallel lines on diagrams
identify and name pairs of parallel
lines using the symbol for 'is
parallel to'

), eg
Students could explore the results about angles
associated with parallel lines cut by a
transversal by starting with corresponding
angles – move one vertex and all four angles to
the other vertex by a translation.
, eg
define and identify 'transversals',
including transversals of parallel
http://www.mathopenref.com/parallel.html
www.mathsisfun.com/geometry/parallel-lines
www.mathplanet.com/education/geometry
Using a diagram similar to the one below,
students could be asked to find the values of
each pronumeral and give reason, given one of
them.
http://www.bbc.co.uk/schools/gcsebitesize/maths/geometry/parallellinesrev1.shtml
lines

identify, name and measure
alternate angle pairs, corresponding
angle pairs and co-interior angle
pairs for two lines cut by a
Draw a pair of parallel lines, students can rule
their own transversal and then measure each
Rulers, protractor
angle.
transversal

use dynamic geometry software to
investigate angle relationships formed

by parallel lines and a
transversal (Problem Solving,

Reasoning)


recognise the equal and
supplementary angles formed when
a pair of parallel lines is cut by a
recognise and explain why adjacent angles
adding to 90º form a right angle
recognise and explain why adjacent angles
adding to 180º form a straight angle
recognise and explain why adjacent angles
adding to 360º form a complete revolution
find the unknown angle in a diagram using
angle results, giving reasons
transversal
Investigate conditions for two lines to
be parallel (ACMMG164)

use angle properties to identify
parallel lines

explain why two lines are either
parallel or not parallel, giving a reason

(Communicating, Reasoning)
apply angle results to construct a pair of parallel
lines using a ruler and a protractor, a ruler and a
set square, or a ruler and a pair of compasses
apply angle and parallel line results to
determine properties of two-dimensional shapes
such as the square, rectangle, parallelogram,
rhombus and trapezium
identify parallel and perpendicular lines in the
environment
http://www.mathopenref.com/parallel.html
apply geometrical facts, properties and
relationships to solve numerical problems such
as finding unknown sides and angles in
diagrams
Eratosthenes’ calculation of the circumference
of the earth used parallel line results.
Solve simple numerical problems
using reasoning (ACMMG164)

Find the value of each variable and give reason.
find the sizes of unknown angles
embedded in diagrams using angle
relationships, including angles at a
point and angles associated with
parallel lines, giving reasons
explain how the size of an unknown 
angle was calculated (Communicating,
Reasoning)



Emphasise to the students when answering
questions on angles, remember the following
points:
Look out for parallel lines (squares, rectangles,
parallelograms and marked parallel lines) and
see which of the above rules apply.
Look out for lines of equal length. Remember
that an isosceles triangle has two sides of equal
length and that the angles which are directly
opposite these sides are also equal.
Diagrams are unlikely to be drawn to scale, so
do not be tempted to measure!
Do not assume things which may turn out to be
untrue (for example, an angle is not necessarily
a right angle just because it looks as though it
should be!).
It is likely that you will not be able to find the
required angle immediately. Do not worry - just
write as much information as possible onto the
diagram. It should eventually lead you to the
answer. If not, you might still get some marks
for your working!

Registration
Evaluation
Class: __________________________
Start Date: _______________________
Finish Date: ______________________
Teacher’s Signature: _______________________
Sample questions
Highlight the response that best describes your view to the following statements and provide comments in the spaces provided.
1. The set text/s (if relevant) were suitable for the student needs and interests:
STRONGLY AGREE
2.
AGREE
UNSURE
STRONGLY DISAGREE
There were sufficient and suitable resources to teach the unit:
STRONGLY AGREE
AGREE
UNSURE
STRONGLY DISAGREE
3.
There was sufficient time to teach the set content:
STRONGLY AGREE
4.
AGREE
UNSURE
STRONGLY DISAGREE
Assess the degree to which syllabus outcomes have been demonstrated by students in this unit:
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5.
Evaluate the degree to which the diverse needs of learners have been addressed in this unit:
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6.
Comment on the effectiveness of pedagogical practices employed in this unit:
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7.
Assessment was meaningful and appropriate to reflect student learning and achievement:
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8.
Suggested program adjustments / other comments:
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