Chapter 7 Geometry

1
WORK PROGRAM
Chapter 7 Geometry
Strand: Space and geometry
Substrands and outcomes:
Two-dimensional space
Two-dimensional space
Angles
Properties of geometrical figures
Section
Are you ready? (page 260)
SGS3.2a Manipulates, classifies and draws two-dimensional shapes and describes side and angle properties
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
GC tips, Investigations,
History of mathematics,
Maths Quest challenge,
10 Quick Questions,
Code puzzles
SkillSHEETs,
Technology applications
WorkSHEETs, Interactive
(CD–ROM)
games, Test yourself,
Topic tests
(CD–ROM)
SkillSHEETs (page 260)
7.1: Classifying angles
7.2: Classifying triangles
according the lengths of
their sides
7.3: Naming angles
7.5: Complementary
angles
7.6: Supplementary angles
7.7: More angle relations
Learning outcomes
SGS3.2a
 naming isosceles,
equilateral and scalene
triangles
SGS3.2b
 classifying angles as
right, acute, obtuse,
reflex, straight or a
revolution
SGS4.2
 naming angles using
A and XYZ
notation
 identifying angles of a
complete revolution,
embedded in a diagram
 using the words
2
Triangles (page 261)
WE 1a-b, 2
Ex 7A Triangles
(page 264)
History of mathematics:
Euclid (page 266)
SkillSHEET 7.1:
Classifying angles
(page 264)
SkillSHEET 7.2:
Classifying triangles
according to the lengths
of their sides
(page 264)
Cabri geometry:
Classifying triangles
(sides) (page 262)
Cabri geometry:
Classifying triangles
(angles) (page 262)
Cabri geometry:
Classifying triangles
(sides) (page 264)
Cabri geometry:
Classifying triangles
(angles) (page 264)
Mathcad: Classifying
triangles (page 264)
‘complementary’ and
‘supplementary’ for
angles adding up to 90
and 180 respectively,
and the terms
‘complement’ and
‘supplement’
 establishing and using
the equality of
vertically opposite
angles
SGS4.3
 naming triangles (eg
ABC) in text
SGS3.2a
 identifying and naming
right-angled triangles
 manipulating,
identifying and naming
isosceles, equilateral
and scalene triangles
 comparing and
describing side
properties of isosceles,
equilateral and scalene
triangles
 exploring by
measurement angle
properties of isosceles,
equilateral and scalene
triangles
 explaining
3
Angles in a triangle
(page 267)
WE 3, 4, 5, 6
SkillSHEET 7.3: Naming
angles (page 269)
SkillSHEET 7.4: Angles in
Cabri geometry: Angle
sum of a triangle
(page 269)
classification of twodimensional shapes
(Communicating)
SGS4.2
 using the common
conventions to indicate
right angles and equal
angles on diagrams
SGS4.3
 labelling and naming
triangles (eg ABC) in
text and on diagrams
 using the common
conventions to mark
equal intervals on
diagrams
 recognising and
classifying types of
triangles on the basis of
their properties
 constructing various
types of triangles using
geometrical
instruments, given
different information
 recognising that a
given triangle may
belong to more than
one class (Reasoning)
SGS4.2
 labelling and naming
angles using A and
4
Ex 7B Angles in a triangle
(page 269)
Exterior angles of a
triangle (page 271)
WE 7a-b, 8, 9, 10
Ex 7C Exterior angles of a
triangle (page 274)
a triangle (page 269)
Investigation: Exterior
angles of a triangle
(page 272)
Investigation: Sum of
exterior angles
(page 276)
Game time 001 (page 275)
Mathcad: Angles in a
triangle (page 269)
Cabri geometry: Angles in
right-angled triangles
(page 269)
Cabri geometry: Exterior
angles of a triangle
(page 272)
Cabri geometry: Exterior
angles of a triangle
(page 274)
Mathcad: Exterior angles
of a triangle (page 274)
XYZ notation
using dynamic
geometry software to
investigate angle
relationships (Applying
strategies, Reasoning)
SGS4.3
 justifying informally
by paper folding or
cutting, and testing by
measuring, that the
interior angle sum of a
triangle is 180
 applying geometrical
facts, properties and
relationships to solve
numerical problems
such as finding
unknown angles in
diagrams (Applying
strategies)
SGS4.2
 labelling the vertex and
arms of an angle with
capital letters
 labelling and naming
angles using A and
XYZ notation
 using dynamic
geometry software to
investigate angle

5
Quadrilaterals (page 276)
WE 11a-b
Ex 7D Quadrilaterals
(page 278)
Maths Quest challenge:
Q1-2 (page 279)
Investigation: Forming
quadrilaterals
(page 279)
10 Quick Questions 1
(page 280)
WorkSHEET 7.1
(page 279)
Cabri geometry: Squares
(page 276)
Cabri geometry:
Rectangles (page 276)
Cabri geometry:
Rhombuses (page 276)
Cabri geometry:
Parallelograms
(page 276)
Cabri geometry:
Trapeziums (page 277)
relationships (Applying
strategies, Reasoning)
SGS4.3
 justifying informally
by paper folding or
cutting, and testing by
measuring, that the
interior angle sum of a
triangle is 180, and
that any exterior angle
equals the sum of the
two interior opposite
angles
 applying geometrical
facts, properties and
relationships to solve
numerical problems
such as finding
unknown angles in
diagrams (Applying
strategies)
SGS3.2a
 exploring by
measurement angle
properties of squares,
rectangles,
parallelograms and
rhombuses
 using templates, rulers,
set squares and
protractors to draw
regular and irregular
6
Cabri geometry: Kites
(page 277)
Cabri geometry: Types of
quadrilaterals (page 278)
Mathcad: Classifying
quadrilaterals (page 278)
two-dimensional
shapes
 identifying and
drawing diagonals on
two-dimensional
shapes
 comparing and
describing diagonals of
different twodimensional shapes
 explaining
classification of twodimensional shapes
(Communicating)
SGS4.2
 using common symbols
for ‘is parallel to’ (  )
and ‘is perpendicular
to’ (  )
 using dynamic
geometry software to
investigate angle
relationships (Applying
strategies, Reasoning)
SGS4.3
 using the common
conventions to mark
equal intervals on
diagrams
 constructing various
types of quadrilaterals
 investigating the
7
Angles in a quadrilateral
(page 281)
WE 12, 13, 14
Ex 7E Angles in a
quadrilateral (page 283)
Code puzzle (page 285)
Cabri geometry: Angles in
a quadrilateral (page
281)
Mathcad: Angles in a
quadrilateral (page 283)
Cabri geometry: Angle
sum of a quadrilateral
(page 283)
Cabri geometry: Angles in
a quadrilateral (page
283)
properties of special
quadrilaterals
 investigating the line
symmetries and the
order of rotational
symmetry of the
special quadrilaterals
 classifying special
quadrilaterals on the
basis of their properties
SGS4.2
 using dynamic
geometry software to
investigate angle
relationships (Applying
strategies, Reasoning)
SGS4.3
 distinguishing between
convex and nonconvex quadrilaterals
 establishing that the
angle sum of a
quadrilateral is 360
 investigating the
properties of special
quadrilaterals
 applying geometrical
facts, properties and
relationships to solve
numerical problems
such as finding
unknown angles in
8
Using equations to
calculate the size of
angles (page 286)
WE 15a-b, 16a-c
Ex 7F Using equations to
calculate the size of
angles (page 288)
SkillSHEET 7.5:
Complementary angles
(page 288)
SkillSHEET 7.6:
Supplementary angles
(page 288)
SkillSHEET 7.7: More
angle relations
(page 288)
Cabri geometry:
Vertically opposite
angles (page 287)
diagrams (Applying
strategies)
SGS3.2b
 identifying angle types
at intersecting lines
SGS4.2
 identifying and naming
adjacent angles,
vertically opposite
angles, straight angles
and angles of complete
revolution, embedded
in a diagram
 using the words
‘complementary’ and
‘supplementary’ for
angles adding up to 90
and 180 respectively,
and the terms
‘complement’ and
‘supplement’
 establishing and using
the equality of
vertically opposite
angles
 finding the unknown
angle in a diagram
using angle results,
giving reasons
(Applying strategies,
Reasoning)
 using dynamic
9
Angles and parallel lines
(page 289)
WE 17a-b, 18
Ex 7G Angles and parallel
lines (page 292)
Investigation: Angle
Game time 002 (page 295)
relationships with
WorkSHEET 7.2
parallel lines (page 290)
(page 295)
Maths Quest challenge:
Q1-3 (page 295)
10 Quick Questions 2
(page 296)
Investigation: Geometry in
architecture (page 297)
Cabri geometry:
Corresponding angles
(page 289)
Cabri geometry:
Co-interior angles
(page 290)
Cabri geometry: Alternate
angles (page 290)
Cabri geometry: Parallel
lines (page 290)
Cabri geometry: Parallel
lines (page 292)
geometry software to
investigate angle
relationships (Applying
strategies, Reasoning)
SGS4.2
 labelling and naming
angles using A and
XYZ notation
 identifying and naming
a pair of parallel lines
and a transversal
 using common symbols
for ‘is parallel to’ (  )
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 cointerior angle pairs for
two lines cut by a
transversal
 recognising the equal
and supplementary
angles formed when a
pair of parallel lines are
10
Angle review (page 298)
Ex 7H Angle review
(page 299)
WorkSHEET 7.3
(page 301)
cut by a transversal
 using angle properties
to identify parallel lines
 using angle
relationships to find
unknown angles in
diagrams
 finding the unknown
angle in a diagram
using angle results,
giving reasons
(Applying strategies,
Reasoning)
 using dynamic
geometry software to
investigate angle
relationships (Applying
strategies, Reasoning)
SGS4.2
 identifying and naming
adjacent angles,
vertically opposite
angles, straight angles
and angles of complete
revolution, embedded
in a diagram
 using the words
‘complementary’ and
‘supplementary’ for
angles adding up to 90
and 180 respectively,
and the terms
11
‘complement’ and
‘supplement’
 establishing and using
the equality of
vertically opposite
angles
 identifying, naming
and measuring 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
 using angle
relationships to find
unknown angles in
diagrams
 finding the unknown
angle in a diagram
using angle results,
giving reasons
(Applying strategies,
Reasoning)
SGS4.3
12


Summary (page 302)
Chapter review (page 304)
‘Test yourself’ multiple
choice questions
(page 306)
Topic tests (2)
using a parallel line
construction, to prove
that the interior angle
sum of a triangle is
180
proving, using a
parallel line
construction, that any
exterior angle of a
triangle is equal to the
sum of the two interior
opposite angles