Space & Geometry - Angles
Syllabus Reference Content Page: 153
Outcome: SGS 4.2
Key Ideas:
Identifies and names angles formed by the intersection
of straight lines, including those related to transversals
on sets of parallel lines, and makes use of the
relationships between them
Classify angles and determine angle relationships
Construct parallel and perpendicular lines and
determine associated angle properties
Complete simple numerical exercise based on geometric
properties
Prior Outcome: SGs 3.2b
Post Outcome: SGS 4.3
p 152
p 154
Classifies, constructs and determines the properties
of triangles and quadrilaterals
Measures, constructs and classifies angles
Working Mathematically Outcomes
Questioning
Applying Strategies
Communicating
Reasoning
Reflecting
Asks questions that
could be explored
using mathematics in
relation to angles
Analyses a mathematical or
real-life situation solving
problems using technology
where appropriate
Uses mathematical
terminology and
notation, algebraic
symbols, diagrams,
text and tables to
communicate
mathematical ideas
Identifies
relationships and the
strengths and
weaknesses of
different strategies
and solutions, giving
reasons
Links mathematical
ideas and makes
connections with and
generalisations about,
existing knowledge and
understanding in
relation to angles
Knowledge and Skills
Students learn about
Working Mathematically
Students learn to
Angles at a Point
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labelling and naming points, lines and intervals using
capital letters
labelling the vertex and arms of an angle with
capital letters
labelling and naming angles using A and XYZ
notation
using the common conventions to indicate right
angles and equal angles on diagrams
identifying and naming adjacent angles (two angles
with a common vertex and a common arm), vertically
opposite angles, straight angles and angles of
complete revolution, embedded in a diagram
using the words ‘complementary’ and ‘supplementary’
for angles adding to 90˚ and 180˚ respectively, and
the terms ‘complement’ and ‘supplement’
establishing and using the equality of vertically
opposite angles
Pendle Hill HS Stage 4 mathematics program 2004
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recognise and explain why adjacent angles adding
to 90˚ form a right angle (Reasoning)
recognise and explain why adjacent angles adding
to 180˚ form a straight line (Reasoning)
recognise and explain why adjacent angles adding
to 360˚ form a complete revolution (Reasoning)
find the unknown angle in a diagram using angle
results, giving reasons (Applying Strategies,
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
(Applying Strategies)
apply angle and parallel line results to determine
properties of two-dimensional shapes such as the
square, rectangle, parallelogram, rhombus and
trapezium (Applying Strategies, Reasoning,
Reflecting)
identify parallel and perpendicular lines in the
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environment (Reasoning, Reflecting)
Angles Associated with Transversals
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identifying and naming a pair of parallel lines and a
transversal
using common symbols for ‘is parallel to’ (ll) and ‘is
perpendicular to’ ( )
using the common conventions to indicate parallel
lines on diagrams
identifying, naming and measuring the alternate
angle pairs, the corresponding angle pairs and the
co-interior angle pairs for two lines cut by a
transversal
using angle properties to identify parallel lines
using angle relationships to find unknown angles in
diagrams
Technology
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construct a pair of perpendicular lines using a ruler
and a protractor, a ruler and a set square, or a
ruler and a pair of compasses (Applying Strategies)
use dynamic geometry software to investigate
angle relationships (Applying Strategies, Reasoning)
Links
Quadrilaterals, geometric proofs.
Resources
Language
Compass, ruler, protractor,
Points, line, intervals, angle, arm, vertex, adjacent,
acute, obtuse, reflex, revolution, complementary,
supplementary, vertically opposite, right, parallel,
alternate, corresponding, co-interior, perpendicular,
protractor, compass
Pendle Hill HS Stage 4 mathematics program 2004
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Learning Experiences and Assessment Opportunities
Assessment for learning
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Students brainstorm all they know about angles. Teacher observes product and determines level of
knowledge. Posters displayed in classroom
Students, in small groups, complete card match activity. Students match the diagram of an angle with its
correct name. Teacher listens to group discussion
At Stage 2 students are expected to be able to:
 describe angles using everyday language and the term “right”
 compare angles using informal means
At Stage 3 srudents are expected to be able to:
 classify angles as right, acute, obtuse, reflex, straight or a revolution
 measure angles in degrees
 construct angles using a protractor
Through a series of graded activities and worksheets students:
 learn how to name points, lines and intervals using capital letters
 name and label vertex and arms of an angle with capital letters
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name and label angles using appropriate notation
Through the use of card-match activities, worksheets and literacy exercises to further emphasise the specific
terminology associated with angles students:
 measure angles using protractor
 identify and label adjacent, vertically opposite and straight angles
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find unknown angles associated with complementary and supplementary angles
By demonstrating through board work and by using worksheets and geometrical instruments students:
 identify parallel lines
 use appropriate symbols for parallel and perpendicular lines
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construct parallel lines
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construct perpendicular lines using a ruler and protractor and set of compasses
Through the use of card-match activities, worksheets and cube-saw students:
 identify alternate, corresponding and co-interior angles on parallel lines
 identify equal and supplementary angles on parallel lines
 find unknown angles on parallel lines
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use appropriate setting out eg x = 73˚ (alternate angles on parallel lines AB CD)
Students use literacy exercises such as card-matches, cloze passages and crosswords to practice the specific
terminology associated with angles.
Pendle Hill HS Stage 4 mathematics program 2004
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