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Maths Quest 10 for New South Wales 5.3 Pathway
Work Programs
Chapter 5
Deductive geometry
Strand: Space and geometry
Substrands and outcomes:
Properties of geometrical figures
Properties of geometrical figures
Properties of geometrical figures
Deductive geometry
Deductive geometry
Deductive geometry
Section
Are you ready? (page 166)
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
SGS5.2.2 Develops and applies results for proving that triangles are congruent or similar
SGS5.3.1 Constructs arguments to prove geometrical results
SGS5.3.2 Determines properties of triangles and quadrilaterals using deductive reasoning
SGS5.3.3 Constructs geometrical arguments using similarity tests for triangles
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 166)
5.1: Naming angles, lines
and figures
5.2: Corresponding sides
and angles of congruent
triangles
5.4: Writing similarity
statements
1
Technology applications
(CD ROM)
Learning outcomes
SGS4.3
 labelling and naming
triangles in text and on
diagrams
 investigating the
properties of special
quadrilaterals
SGS4.4
5.6: Identifying
quadrilaterals
Congruence review
(page 167)
WE 1, 2, 3
Ex 5A Congruence review
(page 169)
SkillSHEET 5.1: Naming
angles, lines and figures
(page 169)
SkillSHEET 5.2:
Corresponding sides
and angles of congruent
triangles (page 169)
SkillSHEET 5.3: Angles
and parallel lines
(page 171)
2
Cabri geometry:
Congruent triangles
(page 167)
Mathcad: Congruence
(page 170)
 matching sides and
angles of two congruent
polygons
SGS5.2.2
 identifying the elements
preserved in similar
triangles, namely angle
size and the ratio of
corresponding sides
SGS5.2.2
 determining what
information is needed to
show that two triangles
are congruent
SSS, SAS, AAS, RHS
 applying the congruency
tests to justify that two
triangles are congruent
 applying the four
triangle congruency tests
in numerical exercises to
find unknown sides and
angles
SGS5.3.1
 determining minimum
conditions to deduce two
triangles are congruent
 writing formal proofs of
congruence of triangles,
preserving matching
order of vertices
 proving statements about
geometrical figures
(Reasoning, Applying
strategies,
Similarity review
(page 172)
WE 4a-c, 5
Ex 5B Similarity review
(page 175)
Code puzzle (page 177)
SkillSHEET 5.4: Writing
similarity statements
(page 176)
SkillSHEET 5.5:
Calculating unknown
sides in a pair of similar
triangles (page 176)
Game time 001 (page 176)
WorkSHEET 5.1
(page 176)
3
Cabri geometry: Similar
triangles (page 172)
Cabri geometry: Similar
triangles (page 175)
Mathcad: Similarity
(page 176)
Communicating)
SGS5.2.2
 identifying the elements
preserved in similar
triangles, namely angle
size and the ratio of
corresponding sides
 determining whether
triangles are similar
 applying the
enlargement or reduction
factor to find unknown
sides in similar triangles
 calculating unknown
sides in a pair of similar
triangles
SGS5.3.3
 determining what
information is needed to
establish that two
triangles are similar
 writing formal proofs of
similarity of triangles in
the standard four- or
five-line format,
preserving the matching
order of vertices,
identifying the similarity
factor when appropriate,
and drawing relevant
conclusions from this
similarity
 proving and applying
further theorems using
similarity, in particular:
Congruence and triangles
(page 178)
WE 6, 7
Ex 5C Congruence and
triangles (page 179)
The interval joining the
midpoints of two sides of
a triangle is parallel to the
third side and half its
length.
Conversely, the line
through the midpoint of a
side of a triangle parallel
to another side bisects the
third side.
 proving statements about
geometrical figures
(Reasoning,
Communicating, Applying
strategies)
SGS5.2.2
 applying congruent
triangle results to
establish properties of
isosceles and equilateral
triangles
SGS5.3.1
 determining minimum
conditions to deduce two
triangles are congruent
 writing formal proofs of
congruence of triangles,
preserving matching
order of vertices
 constructing and writing
geometrical arguments
to prove a general
geometrical result,
giving reasons at each
step of the argument
Investigation: Proving
Pythagoras’ theorem
(page 180)
10 Quick Questions 1
(page 181)
4
 solving Euclidean
geometry problems
 proving Pythagoras’
theorem and applying it
in geometric contexts
 applying the converse of
Pythagoras’ theorem
 proving statements about
geometrical figures
(Reasoning,
Communicating, Applying
strategies)
 solving problems using
deductive reasoning
(Reasoning, Applying
strategies)
SGS5.3.2
 proving properties of
isosceles and equilateral
triangles from the formal
definitions of the shapes
 proving and applying
theorems and properties
related to triangles
 applying theorems and
properties of triangles to
solve problems,
justifying solutions using
deduction (Applying
strategies, Reasoning)
 using and interpreting
formal definitions when
presenting a deductive
argument (Applying
strategies, Reasoning,
5
Quadrilaterals: definitions
and properties
(page 182)
WE 8a-c
Ex 5D Quadrilaterals:
definitions and
properties (page 184)
Investigation: Geometry
and pool (page 185)
SkillSHEET 5.6:
Identifying
quadrilaterals
(page 184)
Game time 002
(page 185)
WorkSHEET 5.2
(page 185)
Quadrilaterals and proof
(page 186)
Maths Quest challenge
Q1-2 (page 189)
WorkSHEET 5.3
(page 189)
6
Cabri geometry:
Trapeziums (page 182)
Cabri geometry:
Parallelograms
(page 182)
Cabri geometry:
Rhombuses (page 182)
Cabri geometry:
Rectangles (page 182)
Cabri geometry: Squares
(page 182)
Cabri geometry: Types of
quadrilaterals (page 184)
Communicating)
SGS5.2.2
 using dynamic geometry
software to investigate
the properties of
geometrical figures
(Applying strategies,
Reasoning)
SGS5.3.2
 stating a definition as the
minimum amount of
information needed to
identify a particular
figure
 proving and applying
tests for quadrilaterals
 reasoning that any result
proven for a
parallelogram would
also hold true for a
rectangle (Reasoning)
 giving reasons why a
square is a rhombus, but
a rhombus is not
necessarily a square
(Reasoning)
 applying theorems and
properties of triangles
and quadrilaterals to
solve problems,
justifying solutions using
deduction (Applying
strategies, Reasoning)
SGS5.2.2
 applying congruent
WE 9, 10
Ex 5E Quadrilaterals and
proof (page 188)
Summary (page 191)
Chapter review (page 192)
10 Quick Questions 2
(page 190)
triangle results to
establish some of the
properties of special
quadrilaterals, including
diagonal properties e.g.
the diagonals of a
parallelogram bisect
each other
SGS5.3.1
 constructing and writing
geometrical arguments
to prove a general
geometrical result,
giving reasons at each
step of the argument
 solving Euclidean
geometry problems
 proving statements about
geometrical figures
(Reasoning,
Communicating, Applying
strategies)
 solving problems using
deductive reasoning
(Reasoning, Applying
strategies)
 making, refining and
testing conjectures
(Questioning, Reasoning,
Reflecting, Applying
strategies)
‘Test yourself’ multiple
choice questions
Topic tests (2)
7