Download Chapter 9 Geometry

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WORK PROGRAM  MQ 9 NSW 5.2 Pathway
Chapter 9 Geometry
Strand: Space and geometry
Substrands and outcomes:
Two-dimensional space
SGS3.2b Measures, constructs and classifies angles
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
Properties of geometrical figures
SGS4.3 Classifies, constructs and determines the properties of triangles and quadrilaterals
Properties of geometrical figures
SGS5.2.1 Develops and applies results related to the angle sum of interior and exterior angles for any
convex polygon
Section
Are you ready? (page 310)
GC tips, Investigations,
History of mathematics,
Maths Quest challenge,
10 Quick Questions,
Code puzzles
SkillSHEETS,
WorkSHEETS,
Interactive games,
Test yourself, Topic tests
(CD–ROM)
SkillSHEETS (page 310)
9.1: Naming angles
9.2: Classifying angles
9.3: Complementary and
supplementary angles
9.4: More angle relations
9.5: Angles in a triangle
9.7: Angles and parallel
lines
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
revolution, embedded
in a diagram
2

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
that the interior angle
sum of a triangle is
3
Angle review (page 311)
WE 1a-b, 2a-b
Ex 9A Angle review
(page 315)
SkillSHEET 9.1: Naming
angles (page 315)
SkillSHEET 9.2:
Classifying angles
(page 315)
SkillSHEET 9.3:
Complementary and
supplementary angles
(page 315)
SkillSHEET 9.4: More
angle relations
(page 315)
SkillSHEET 9.5: Angles in
a triangle (page 316)
SkillSHEET 9.6: Angle
sum of a quadrilateral
(page 316)
180º, and that any
exterior angle equals
the sum of the two
interior opposite angles
Cabri geometry: Vertically SGS3.2b
opposite angles
 classifying angles as
(page 312)
right, acute, obtuse,
Mathcad: Angle review
reflex, straight or a
(page 315)
revolution
Mathcad: Angle sum
SGS4.2
(page 316)
 labelling and naming
Cabri geometry: Angle
angles using A and
sum of a triangle
XYZ notation
(page 316)
 using the common
conventions to indicate
right angles and equal
angles on diagrams
 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 to 90º
and 180º respectively,
and the terms
‘complement’ and
‘supplement’
4

Angles and parallel lines
(page 317)
WE 3a-b, 4
Ex 9B Angle and parallel
lines (page 319)
Code puzzle (page 320)
SkillSHEET 9.7: Angles
and parallel lines
(page 319)
Cabri geometry: Parallel
lines (page 317)
Cabri geometry:
Corresponding angles
(page 317)
Cabri geometry: Alternate
angles (page 317)
Cabri geometry:
Co-interior angles
(page 317)
establishing and using
the equality of
vertically opposite
angles
SGS4.3
 using the common
conventions to mark
equal intervals on
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
 establishing that the
angle sum of a
quadrilateral is 360
SGS4.2
 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
5

Other polygons (page 321)
WE 5, 6a-b, 7
Ex 9C Other polygons
(page 324)
Investigation: Sum of
angles in a polygon
(page 321)
Investigation: Angles in a
regular polygon
(page 323)
Investigation:
Parliamentary question
time (page 325)
SkillSHEET 9.8: Angle
sum of a polygon
(page 324)
Game time 001 (page 325)
WorkSHEET 9.1
(page 325)
Mathcad: Angles in
polygons (page 324)
Cabri geometry: Angle
sum of a polygon
(page 324)
Cabri geometry: Exterior
angles of a polygon
(page 325)
using angle properties
to identify parallel
lines
 using angle
relationships to find
unknown angles in
diagrams
 using dynamic
geometry software to
investigate angle
relationships (Applying
strategies, Reasoning)
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
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
6
Constructing and drawing
triangles (page 326)
WE 8, 9, 10
Ex 9D Constructing and
drawing triangles
(page 328)
10 Quick Questions 1
(page 330)
Maths Quest challenge:
Q1-2 (page 330)
SkillSHEET 9.9:
Cabri geometry: Three
Constructing angles
sides (page 328)
with a protractor
Cabri geometry: Two
(page 328)
angles and a side
SkillSHEET 9.10: Drawing
(page 328)
a diagram from given
Cabri geometry: Two
information (page 329)
sides and an angle
between (page 329)
Further sketching and
constructing (page 331)
Maths Quest challenge:
Q1 (page 337)
WorkSHEET 9.2
(page 337)
Cabri geometry: Two
sides and an angle
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)
 constructing various
types of triangles using
geometrical
instruments, given
different information
 sketching and labelling
triangles from a given
verbal description
(Communicating)
SGS4.2
 applying angle results
7
WE 11, 12, 13, 14, 15, 16
Ex 9E Further sketching
and constructing
(page 336)
10 Quick Questions 2
(page 338)
between (page 336)
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
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
8
Constructing polygons
(page 339)
WE 17, 18, 19, 20, 21
Ex 9F Constructing
polygons (page 345)
Game time 002 (page 345)
WorkSHEET 9.3
(page 345)
Summary (page 346)
Chapter review (page 347)
‘Test yourself’ multiple
choice questions
(page 348)
Topic tests (2)
Cabri geometry: Star
polygons (page 343)
Cabri geometry:
Circumcentre (page 345)
Cabri geometry: Centroid
(page 345)
Cabri geometry: Incentre
(page 345)
(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
angles of 60º and 120º
by applying
geometrical properties
(Applying strategies)
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)