Maths Quest 10 for New South Wales 5.3 Pathway

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Oct 10, 2013 (4 years and 2 months ago)

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Maths Quest 10 for New South Wales 5.3 Pathway


Work Programs


Chapter 15

Circle
g
eometry

Strand
:

Space and geometry

Substrands and outcomes
:

Properties of geometrical figures

SGS4.3

Classifies, constructs and determines the pr
operties of triangles and quadrilaterals

Properties of geometrical figures

SGS4.4

Identifies congruent and similar two
-
dimensional figures stating the relevant conditions

Properties of geometrical figures

SGS5.2.2

Develops and applies results for proving t
hat triangles are congruent or similar

Deductive geometry



SGS5.3.1

Constructs arguments to prove geometrical results

Circle geometry



SGS5.3.4

Applies deductive reasoning to prove circle theorems and to solve problems


Section

GC tips, Investigations,

History of mathematics,
Maths Quest
c
hallenge,

10 Quick Questions,

Code
p
uzzles,

Career profiles

SkillSHEETS,
WorkSHEETS,

Interactive games,

Test

yourself, Topic tests
(CD ROM)


Technology applications

(CD ROM)

Learning
o
utcomes

Are you ready? (pag
e 542)


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 a
rc
length


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 whet
her
triangles are similar

SGS4.3



applying geometric
facts, properties and
re
lationships to solve
numerical problems
such as finding
unknown sides and
ang
les in diagrams

Introduction (page 543)

Angles in a circle
(page

545)

WE 1, 2, 3

Ex 15A Angles in a circle
(page 549)

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
g
eometry
: Angles at
the centre and the
circumference
(page

545)

Cabri
g
eometry
: Angles at

the centre and the
circumference


proof
(page 545)

Cabri
g
eometry
: Angles
subtended by the same
arc (page 546)

Cabri
g
eometry
: Tangents
SGS5.3.1



constructing and writing
geometrical arguments
to prove a general
geometrical result,
giving reaso
ns 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, s
egment,
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
stan
ds



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
(
Applyin
g strategies
,
Reasoning
)



applying circle
theorems to find
unknown angles and
sides in diagrams
(
Applying strategies
,
Reasoning
)



constructing tangents to
a circle (
Applying
strategies
)

Intersecting chords,
secants and tangents
(page 552)

WE 4, 5, 6, 7

Ex 1
5B 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 56
1)


Cabri
g
eometry
:
Intersecting chords
(page 552)

Cabri
g
eometry
:
Intersecting secants
(page 553)

Cabri
g
eometry
:
Intersecting tangents
(page 554)

Cabri
g
eometry
: Chords
(page 555)

SGS5.3.4



using the
tangent to a
circle

result as an
assumption when
provin
g theorems
involving tangents



proving and applying
the theorems

on
:

-

c
hord properties


-

a
ngle properties




-

tangents and secants



applying circle
theorems to find
unknown sides in
diagrams (
Applying
strategies
,
Reasoning
)

Cyclic quadrilat
erals
(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)

G
ame

time
001 (page

564)

WorkSHEET

15.2
Cabri
g
eometry
: Cyclic
quadrilaterals I
(page

561)

Cabri
g
eometry
: Cyclic
quadrilaterals II


proof
SGS5.3.4



proving and applying
the theorems on:


-

chord properties


-

angle properties

(page

563)

(page

564)

(page 561)

Cabri
g
eometry
: Exterior
angles of cyclic
quadrilaterals
(page

562)


-

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
)

Tangents, secants and
chords (page 565)

WE 10
, 11

Ex 15D Tangents, secants
and chords (page 567)

Maths Quest challenge

Q1
-
2 (page 570)

Investigation
: Circle
constructions
(page

570)


Cabri geometry
: Alternate
segment theorem
(page

565)

SGS5.3.4



using the
tangent to a
circle
result as an
assumption wh
en
proving theorems
involving tangents



proving and applying
the theorems

on
:


-

c
hord properties


-

a
ngle properties




-

tangents and secants



applying circle
theorems to find
unknown angles and
sides in diagrams
(
Applying strategies
,
Reason
ing
)



using circle and other
theorems to prove
geometrical results and
in problem solving
(
Applying strategies
,
Reasoning
)



finding the centre of a
circle by construction
(
Applying strategies
)



constructing tangents to
a circle (
Applying
strategies
)

Great ci
rcles (page 571)

WE 12, 13, 14

Ex 15E Great
c
ircles (page
575)

Investigation
: Greenwich
Mean Time (page 572)

Investigation
: SOS!
(page

576)

10 Quick Questions

2
(page 577)

Maths Quest challenge

Q1
-
2 (page 577)

Investigation
: Eratosthenes
calculates the dia
meter
of the
E
arth
!

(page 578)

SkillSHEET

15.7:
Calculating arc length
(page 575)

WorkSHEET

15.2
(page

576)

G
ame

time
002 (page 576)

Mathcad
: Arc length
(page

575)



using circle and other
theorems to prove
geometrical results and
in problem solving
(
Applyin
g strategies
,
Reasoning
)


Summary (page 579)

Chapter review (page 580)


‘Test
y
ourself’ mult
iple
choice questions

Topic tests (2)