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WORK PROGRAM
Chapter 3 Geometry
Strand: Space and geometry
Substrands and outcomes:
Two-dimensional space
Angles
Properties of geometrical figures
Properties of geometrical figures
Properties of geometrical figures
Deductive geometry
Section
Are you ready? (page 84)
SGS3.2b Measures, constructs and classifies angles
SGS4.2 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
SGS4.3 Classifies, constructs and determines the properties of triangles and quadrilaterals
SGS4.4 Identifies congruent and similar two-dimensional figures stating the relevant conditions
SGS5.2.1 Develops and applies results related to the angle sum of interior and exterior angles for any
convex polygon
SGS5.3.1 Constructs arguments to prove geometrical results
GC tips, Investigations,
History of mathematics,
Maths Quest challenge,
10 Quick Questions,
Code puzzles,
Career profiles
SkillSHEETs,
WorkSHEETs,
Interactive games,
Test yourself, Topic tests
(CD-ROM)
SkillSHEETs (page 84)
3.1: Naming angles
3.2: Classifying angles
3.3: Complementary and
supplementary angles
3.4: More angle relations
3.5: Angles and parallel
lines
3.6: Angles in a triangle
Technology applications
(CD-ROM)
Learning outcomes
SGS3.2b
 classifying angles as
right, acute, obtuse,
reflex, straight or a
revolution
SGS4.2
 labelling and naming
angles using A and
XYZ notation
 identifying adjacent
angles, vertically
opposite angles,
straight angles and
angles of complete
2
revolution, embedded
in a diagram
 using the words
‘complementary’ and
‘supplementary’ for
angles adding to 90
and 180º respectively,
and the terms
‘complement’ and
‘supplement’
 establishing and using
the equality of
vertically opposite
angles
 identifying and naming
the alternate angle
pairs, the
corresponding angle
pairs and the cointerior angle pairs for
two lines cut by a
transversal
 recognising the equal
and supplementary
angles formed when a
pair of parallel lines
are cut by a transversal
 using angle properties
to identify parallel
lines
SGS4.3
 justifying informally
3
Angle review (page 85)
Ex 3A Angle review
(page 88)
Code puzzle (page 91)
SkillSHEET 3.1: Naming
angles (page 88)
SkillSHEET 3.2:
Classifying angles
(page 88)
SkillSHEET 3.3:
Complementary and
supplementary angles
(page 88)
SkillSHEET 3.4: More
angle relations (page 88)
SkillSHEET 3.5: Angles
and parallel lines
(page 89)
SkillSHEET 3.6: Angles in
a triangle (page 90)
SkillSHEET 3.7: Angle
sum of a quadrilateral
(page 90)
that the interior angle
sum of a triangle is
180º, and that any
exterior angle equals
the sum of the two
interior opposite angles
Cabri geometry: Vertically SGS3.2b
opposite angles (page 86)  classifying angles as
Cabri geometry: Parallel
right, acute, obtuse,
lines (page 87)
reflex, straight or a
Cabri geometry:
revolution
Corresponding angles
SGS4.2
(page 87)
 labelling and naming
Cabri geometry: Alternate
angles using A and
angles (page 87)
XYZ notation
Cabri geometry: Co using the common
interior angles (page 87)
conventions to indicate
Mathcad: Angle review
right angles and equal
(page 88)
angles on diagrams
Mathcad: Angle sum
 identifying and naming
(page 90)
adjacent angles (two
Cabri geometry: Angle
angles with a common
sum of a triangle
vertex and a common
(page 90)
arm), vertically
opposite angles,
straight angles and
angles of complete
revolution, embedded
in a diagram
 using the words
‘complementary’ and
‘supplementary’ for
4
angles adding to 90º
and 180º respectively,
and the terms
‘complement’ and
‘supplement’
 establishing and using
the equality of
vertically opposite
angles
 identifying and naming
alternate angle pairs,
corresponding angle
pairs and co-interior
angle pairs for two
lines cut by a
transversal
 recognising the equal
and supplementary
angles formed when a
pair of parallel lines
are cut by a transversal
 using angle properties
to identify parallel
lines
 using angle
relationships to find
unknown angles in
diagrams
SGS4.3
 using the common
conventions to mark
equal intervals on
5
Other polygons (page 92)
WE 1, 2a–b, 3
Ex 3B Other polygons
(page 95)
Investigation: Sum of
angles in a polygon
(page 92)
Investigation: Angles in a
regular polygon
(page 94)
Investigation: Regular
polygons (page 96)
SkillSHEET 3.8: Angle
sum of a polygon
(page 95)
WorkSHEET 3.1 (page 96)
Mathcad: Angles in
polygons (page 95)
Cabri geometry: Angle
sum of a polygon
(page 95)
Cabri geometry: Exterior
angles of a polygon
(page 96)
Cabri geometry: Regular
diagrams
 justifying informally
that the interior angle
sum of a triangle is
180º, and that any
exterior angle equals
the sum of the two
interior opposite angles
 using a parallel line
construction to prove
that the interior angle
sum of a triangle is
180º
 proving, using a
parallel line
construction, that any
exterior angle of a
triangle is equal to the
sum of the two interior
opposite angles
 establishing that the
angle sum of a
quadrilateral is 360º
SGS5.2.1
 applying the result for
the interior angle sum
of a triangle to find, by
dissection, the interior
sum of polygons with
4, 5, 6, 7, 8,  sides
 defining the exterior
angle of a convex
6
polygons (page 96)
Constructing triangles
(page 97)
WE 4, 5, 6
Ex 3C Constructing
triangles (page 99)
10 Quick Questions 1
(page 101)
Maths Quest challenge:
Q1–2 (page 101)
SkillSHEET 3.9:
Constructing angles with
a protractor (page 99)
Game time 001 (page 100)
Cabri geometry: Three
sides (page 99)
Cabri geometry: Two
angles and a side
(page 99)
Cabri geometry: Two
sides and an angle
between (page 100)
polygon
 establishing that the
sum of the exterior
angles of any convex
polygon is 360º
 applying angle sum
results to find
unknown angles
 expressing in algebraic
terms the interior angle
sum of a polygon with
n sides
(Communicating)
 finding the size of the
interior and exterior
angles of regular
polygons with 5, 6, 7,
8, … sides (Applying
strategies)
 solving problems using
angle sum of polygon
results (Applying
strategies)
SGS4.3
 recognising and
classifying types of
triangles on the basis
of their properties
(acute-angled, rightangled, obtuse-angled,
scalene, isosceles and
equilateral triangles)
7

Further sketching and
constructing (page 102)
WE 7, 8, 9, 10, 11, 12
Ex 3D Further sketching
and constructing
(page 107)
Maths Quest challenge:
Q1 (page 108)
Investigation: Fractals
(page 109)
10 Quick Questions 2
(page 111)
WorkSHEET 3.2
(page 108)
Cabri geometry: Two
sides and an angle
between (page 107)
constructing various
types of triangles using
geometrical
instruments, given
different information
 sketching and labelling
triangles and
quadrilaterals from a
given verbal
description
(Communicating)
 recognising that a
given triangle may
belong to more than
one class (Reasoning)
 recognising that the
longest side of a
triangle is always
opposite the largest
angle (Applying
strategies, Reasoning)
SGS4.2
 applying angle results
to construct a pair of
parallel lines using a
ruler and a protractor
or a ruler and a pair of
compasses (Applying
strategies)
 constructing a pair of
perpendicular lines
using a ruler and a pair
8
of compasses
(Applying strategies)
SGS4.3
 constructing various
types of triangles using
geometrical
instruments, given
different information
 constructing various
types of quadrilaterals
 bisecting an angle by
applying geometrical
properties (Applying
strategies)
 bisecting an interval by
applying geometrical
properties (Applying
strategies)
 drawing a
perpendicular to a line
from a point on the
line by applying
geometrical properties
(Applying strategies)
 drawing a
perpendicular to a line
from a point off the
line by applying
geometrical properties
(Applying strategies)
 using ruler and
compasses to construct
9
Constructing polygons
(page 112)
WE 13, 14, 15, 16, 17
Ex 3E Constructing
polygons (page 118)
Game time 002 (page 119)
WorkSHEET 3.3
(page 132)
Cabri geometry: Star
polygons
(pages 116, 119)
Cabri geometry:
Circumcentre (page 118)
Cabri geometry: Centroid
(page 118)
Cabri geometry: Incentre
(page 118)
angles of 60º and 120º
by applying
geometrical properties
(Applying strategies)
SGS4.4
 using dynamic
geometry software to
investigate the
properties of
geometrical figures
(Applying strategies,
Reasoning)
SGS4.3
 constructing various
types of triangles using
geometrical
instruments, given
different information
 constructing various
types of quadrilaterals
 bisecting an interval by
applying geometrical
properties (Applying
strategies)
 drawing a
perpendicular to a line
from a point on the
line by applying
geometrical properties
(Applying strategies)
 drawing a
perpendicular to a line
10
Geometry in architecture,
design and art (page 119)
WE 18, 19, 20a–b
Ex 3F Geometry in
architecture, design and
art (page 124)
Summary (page 126)
Chapter review (page 127)
Investigation: The Golden
Ratio (page 122)
SkillSHEET 3.10: Using
the quadratic formula
(page 125)
‘Test yourself’ multiple
choice questions
(page 128)
Cabri geometry: Golden
rectangle (page 125)
Cabri geometry:
Tessellations (page 125)
from a point off the
line by applying
geometrical properties
(Applying strategies)
SGS5.3.1
 solving Euclidean
geometry problems
 solving problems using
deductive reasoning
(Reasoning, Applying
strategies)
SGS4.4
 recognising congruent
figures in tessellations,
art and design work
(Reflecting)
SGS 5.3.1
 solving Euclidean
geometry problems
 solving problems using
deductive reasoning
(Reasoning, Applying
strategies)
 make, refine and test
conjectures
(Questioning,
Communicating,
Applying strategies,
Reasoning)
11
Topic tests (2)