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Maths Quest 10 for New South Wales 5.3 Pathway
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Chapter 15 Circle geometry
Strand: Space and geometry
Substrands and outcomes:
Properties of geometrical figures
Properties of geometrical figures
Properties of geometrical figures
Deductive geometry
Circle geometry
Section
SGS4.3
SGS4.4
SGS5.2.2
SGS5.3.1
SGS5.3.4
Classifies, constructs and determines the properties of triangles and quadrilaterals
Identifies congruent and similar two-dimensional figures stating the relevant conditions
Develops and applies results for proving that triangles are congruent or similar
Constructs arguments to prove geometrical results
Applies deductive reasoning to prove circle theorems and to solve problems
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)
Technology applications
(CD ROM)
Learning outcomes
Are you ready? (page 542)
Introduction (page 543)
Angles in a circle
(page 545)
WE 1, 2, 3
Ex 15A Angles in a circle
(page 549)
SkillSHEETs (page 542)
15.1: Using tests to prove
congruent triangles
15.2: Corresponding sides
and angles of congruent
triangles
15.3: Using tests to prove
similar triangles
15.4: Angles in a triangle
15.5: More angle relations
15.7: Calculating arc
length
Investigation: Angles in a
circle (page 545)
Investigation: Constructing
a tangent (page 547)
Maths Quest challenge
Q1-3 (page 551)
SkillSHEET 15.1: Using
tests to prove congruent
triangles (page 543)
SkillSHEET 15.2:
Corresponding sides and
angles of congruent
triangles (page 543)
SkillSHEET 15.3: Using
tests to prove similar
triangles (page 543)
SkillSHEET 15.4: Angles
in a triangle (pages 549)
Cabri geometry: Angles at
the centre and the
circumference
(page 545)
Cabri geometry: Angles at
the centre and the
circumference – proof
(page 545)
Cabri geometry: Angles
subtended by the same
arc (page 546)
Cabri geometry: Tangents
SGS5.2.2
 applying the
congruency tests to
justify that two triangles
are congruent
SGS4.4
 matching sides and
angles of two congruent
polygons
SGS5.2.2
 determining whether
triangles are similar
SGS4.3
 applying geometric
facts, properties and
relationships to solve
numerical problems
such as finding
unknown sides and
angles in diagrams
SGS5.3.1
 constructing and writing
geometrical arguments
to prove a general
geometrical result,
giving reasons at each
step of the argument
 proving statements
about geometrical
figures (Reasoning,
Communicating,
Applying strategies)
SkillSHEET 15.5: More
angle relations:
(page 549)
WorkSHEET 15.1
(page 551)
(page 547)
SGS5.3.4
 identifying and naming
parts of a circle (centre,
radius, diameter,
circumference, sector,
arc, chord, secant,
tangent, segment,
semicircle)
 using terminology
associated with angles
in circles such as
subtend, standing on the
same arc, angle at the
centre, angle at the
circumference, angle in
a segment
 identifying the arc on
which an angle at the
centre or circumference
stands
 demonstrating that at
any point on a circle,
there is a unique tangent
to the circle, and that
this tangent is
perpendicular to the
radius at the point of
contact
 applying circle
theorems to prove that
the angle in a semicircle
is a right angle
Intersecting chords,
secants and tangents
(page 552)
WE 4, 5, 6, 7
Ex 15B Intersecting
chords, secants and
tangents (page 557)
Investigation: Intersecting
chords (page 552)
Investigation: Intersecting
secants (page 553)
History of mathematics:
(page 559)
Code puzzle (page 560)
Investigation:
Quadrilaterals in circles
(page 561)
Cyclic quadrilaterals
(page 561)
WE 8, 9
Ex 15C Cyclic
quadrilaterals
10 Quick Questions 1
(page 564)
SkillSHEET 15.6: Angle
sum of a quadrilateral
(page 563)
Game time 001 (page 564)
WorkSHEET 15.2
(Applying strategies,
Reasoning)
 applying circle
theorems to find
unknown angles and
sides in diagrams
(Applying strategies,
Reasoning)
 constructing tangents to
a circle (Applying
strategies)
Cabri geometry:
SGS5.3.4
Intersecting chords
 using the tangent to a
(page 552)
circle result as an
Cabri geometry:
assumption when
Intersecting secants
proving theorems
(page 553)
involving tangents
Cabri geometry:
 proving and applying
Intersecting tangents
the theorems on:
(page 554)
- chord properties
Cabri geometry: Chords
- angle properties
(page 555)
- tangents and secants
 applying circle
theorems to find
unknown sides in
diagrams (Applying
strategies, Reasoning)
Cabri geometry: Cyclic
SGS5.3.4
quadrilaterals I
 proving and applying
(page 561)
the theorems on:
Cabri geometry: Cyclic
- chord properties
quadrilaterals II – proof
- angle properties
(page 563)
Tangents, secants and
chords (page 565)
WE 10, 11
Ex 15D Tangents, secants
and chords (page 567)
(page 564)
Maths Quest challenge
Q1-2 (page 570)
Investigation: Circle
constructions
(page 570)
(page 561)
Cabri geometry: Exterior
angles of cyclic
quadrilaterals
(page 562)
Cabri geometry: Alternate
segment theorem
(page 565)
- tangents and secants
 applying circle
theorems to find
unknown angles in
diagrams (Applying
strategies, Reasoning)
 using circle and other
theorems to prove
geometrical results and
in problem solving
(Applying strategies,
Reasoning)
SGS5.3.4
 using the tangent to a
circle result as an
assumption when
proving theorems
involving tangents
 proving and applying
the theorems on:
- chord properties
- angle properties
- tangents and secants
 applying circle
theorems to find
unknown angles and
sides in diagrams
(Applying strategies,
Reasoning)
 using circle and other
theorems to prove
geometrical results and
Great circles (page 571)
Investigation: Greenwich
WE 12, 13, 14
Mean Time (page 572)
Ex 15E Great circles (page Investigation: SOS!
575)
(page 576)
10 Quick Questions 2
(page 577)
Maths Quest challenge
Q1-2 (page 577)
Investigation: Eratosthenes
calculates the diameter
of the Earth! (page 578)
Summary (page 579)
Chapter review (page 580)
SkillSHEET 15.7:
Calculating arc length
(page 575)
WorkSHEET 15.2
(page 576)
Game time 002 (page 576)
‘Test yourself’ multiple
choice questions
Topic tests (2)
Mathcad: Arc length
(page 575)
in problem solving
(Applying strategies,
Reasoning)
 finding the centre of a
circle by construction
(Applying strategies)
 constructing tangents to
a circle (Applying
strategies)
 using circle and other
theorems to prove
geometrical results and
in problem solving
(Applying strategies,
Reasoning)