# Exercise 9.1

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```					     Exercise 9.1                    Similar ﬁgures
1 These two ﬁgures hav a similar shape.
e

A′                                   B′

A                     B

D                C                               D′                         C′

E          F

H          G                                     E′                F′

J          I                                          H′                G′

Figure 1

J′             I′

Figure 2
a Find the length of AJ in ﬁgure 1.
b Find the length of the matching or corresponding side in ﬁgure 2 and set up the
following ratio:
Length of A′J′
----------------------------------- =
-   or
Length of AJ
c Mak a ratio of the length AB and its corresponding side in ﬁgure 2:
e
Length of A′B′
------------------------------------ =
-   or
Length of AB
d How much larger are all the lengths in ﬁgure 2 than the corresponding lengths in
ﬁgure 1?
e This is called the enlargement or scale factor. Copy and complete the following.
‘Figure 1 has been enlarged by a scale factor of                 to get the similar ﬁgure in
ﬁgure 2.’
2 On dot paper copy these diagrams. Then in each case draw a similar ﬁgure using the
en.
scale factor giv
a                                                b

Scale factor 2                                         Scale factor 4

SIMILARITY AND TRIGONOMETRY    287   CHAPTER 9
c                                                d

1
Scale factor 3                       Scale factor -
2

3 Deciding whether ﬁgures have a similar shape sometimes can be a little more difﬁcult
than it ﬁrst appears.
a Are these logos mathematically similar?

P R      I A

P R I A
Hint: Measure the length and width of the two logos. How many times larger is the
second than the ﬁrst?
b Would you say that the cereal boxes below are mathematically similar; that is, is
one an enlargement of the other?

KORN
KORN                                         BUBBLES
BUBBLES

NE                                         NE
W                                             W
Box I                                     Box II
Hint: Measure the length and width of each box of cereal. How many times higher
is box II than box I? How many times wider is box II than box I? Would you now
say the two boxes are mathematically similar? Explain.

288       NELSON MATHS FOR WESTERN AUSTRALIA, BOOK 2
4 This is a plan of a single-fronted house in Thebarton. The actual size of the lounge is
4500 mm × 4500 mm.

Lounge                                                                                                                                                                                                                                                                                                                                                                                                   Dining                                                                          Kitchen

Bedroom 1                                                                                     Bedroom 2

Bathroom                                                                        Laundry

a Use the diagram to calculate the scale factor linking the plan to the house.
b i Calculate the length of the bathroom.
ii Calculate the maximum width of the house.
iii Calculate the length of the common bedroom wall.
iv Calculate the total length of the L-shaped hallway (longest wall).
5 On this map of Melbourne University the scale is given at the top.
241 Royal Pde.

= 1 cm
Scale: 50 m PALMERSTON PL.

ATHLETICS TRACK
TRINITY COLLEGE
COURTS
SQUASH

ST MARY’S COLLEGE                                                                        308
103
H                                                                                                                                                                                                   BEAUREPAIRE CENTRE                                                                  SPORTS CENTRE

101
Tin              Alley

361                 GATE 14 (exit only)                                                                                                 Tin    Alley
BALDWIN
Tin    Alley                     GATE 1
Student
360                                                                                                  OLD FORESTRY                                                                                                                     Services                                         SPENCER
UNIVERSITY
113                                                                                                         PHYSICS
ELGIN ST
359                                               142                                                109                                                    HOUSE                                                                                                                                                                                                                                                                      192
Union Rd.

112                                                                                                                                                                             115             REDMOND
BARRY
North
THE INSTITUTE OF LAND

358                                                                                                                           BOTANY                                                                                    Court
Foot bridge
EARTH SCIEN
& FOOD RESOURCES

357                                                                                                                                                                                                                                                                                     Union
200              McCOY
GATE 2

System                                                                                                                                                                                                                                                                                                                    192
356                                                                                   Garden                                          122                                                           UNION                                                                               Lawn
HOUSE
130                                                                                                                        ARCHITECTURE,                                                         PHYSICS                                                                  201
Professor’s Walk

THOMAS
CHERRY
BUILDING &
BOTANY                                                                                                                                                                                  132                            PLANNING                                             OLD PATHOLOGY              THE IAN
Student                                                                                                                                                                  POTTER
Deakin
Crt
143                                                                                                                                                                                                                                                                                                   327 INFORMATION
147                                                                                               NATURAL                                                                                                                                                                                                                        134               136                                                           TECHNOLOGY
139                                         PHILOSOPHYOLD PHYSICS                   131                                                                                                                 Disability                                                                                                                                           CENTRE
Liaison
ZOOLOGY

GRAINGER                                                                 BABEL                                                   (BOTANY)                                              RAYMOND
140

128                  BOOK
MUSEUM                                                                                                                                                                   ROOM          PRIESTLEY
152                                                          Unit
GATE 3
343
Masson Road                                                            Pedestrian Entry Only                                                           MAINTENANCE

MAINTENANCE
Law
GATE 13
150                                                                                                                                            OLD 155                                     Mathematics & Statistics
Cussonia

30 mts from
ECONOMICS &                                                                                          Library                                                                                                                                                                   157
COMMERCE                                                          149                                                                                                                                                   154
GEOLOGY                                           160                                                                    312
Court

ain Campus                                                                                                                                                                                                                                    MacFarland
141                                                                                                                                                              Old                                                                                153                                                                                                                                                                                                                  343
CHEMISTRY

OLD ARTS                                            Court
EAST WING

344

CONSERVATORIUM                                                                     148                                                                                                                                                     CHEMISTRY
BERRY                             Traffic &
e insert below)                                     OF MUSIC                                                                                                                                                                                                                                                                                                                                                                                               Security
LAW                                                                                                                                          OLD                                                                           Office
TERINARY                                                                                                                                                                                                                                         151                                                                                                                          GEOLOGY                                                                   A.H. Enquiries
IENCE                                                                              GENETICS                                                                                                                                                                                                                                                                                   SOUTH

WILSON

194                                                                                                                                                                                                                                                                                              156
HALL

GATE 12                                        Genetics Lane                                                     BAILLIEU                                                                                                                                                                                        161                                                                                                          GATE 4
Car
WALTER BOAS

LIBRARY                                                                                                                                                                          C.S.H.E.
Park
Professor’s Walk

(ARTS AND
185                                                     HUMANITIES
Entry                                                                                                                          162       ALICE HOY     SIDNEY
MYER
COLLECTIONS)                                                                                                                                                                                        CHEM.
193                                                              163                          ENG.1                      165                                                               ASIA
CENTRE
BIOCHEMISTRY &                                                                          177
ENGINEERING

South Lawn
& ELECTRONIC
ELECTRICAL

MOLECULAR BIOLOGY                                                                                                                                                                                                                                                                                 Block J                                                                             158
CHEM.ENG.2

GATE 5
Block K

167

195                                                                                            166
164

DOUG
184                                                                                                                                                                                                                          OLD                                                                                          McDONELL             168
Underground
Car Park                                                                            METALLURGY
Wilson Avenue

MICROBIOLOGY
& IMMUNOLOGY                                                                                                                                                                                                                                                                                                                                                                              International
182                                                                                                                                        Block H                                   Block G                                         172        PLAZA                                                    Office &
FRANK       197
Block F

R.M.H.                                                                                                                                       BROWNLESS                                                                                                                                                                                                                                                                                                   Scholarships
LINICAL                          GATE 11                                                                                                       MEDICAL                                                             JOHN
171                      TATE          JOHN                    Office
CIENCES                                                                                                                                        LIBRARY
191                                                                                                           169                                                             189           SMYTH

PHYSIOLOGY

ERC
SWANSTON STREET

MEDLEY
HOWARD                                                                                                                                                                                                                                                                                                                                                        GATE 6
601                                                                          183   FLOREY                                                                                                                                                                                              ENGINEERING
MECH. & MANUF.
ENGINEERING

Block A
199
TRAM No’s 18,19 & 20

173                                                                                           198
Block E

MEDICINE
CENTRE

SCHOOL OF GRAD. STUDIES
08                                                                                                             181
ARTS

PHARMACOLOGY                              ANATOMY &                                                                                  Block B                                Block C                       Block D
R.M.H.
EDICAL
PATHOLOGY                                                       CELL BIOLOGY
187                        175                                        174                                             176
SEARCH                                                                                                                                                                                                                                   GEOMATICS                                      CIVIL & ENVIRONMENTAL                                                170
TRAM No’s 1, 22

ENGINEERING
ROYAL

GATE 10                                                                                GATE 9                                                                  GATE 8                            GATE 7

ROYAL                                                                                                                                                                                         GRATTAN              STREET
DENTAL
OSPITAL                                                                                                                                                                                                                                                                                                            203                                368
MALVINA PL.

700                                                                                                                                                                                                                                                            465                                                                                                                     H
UNIVERSITY SQUARE                                                        UNIVERSITY SQUARE                                                                                                                                                                                  LIT. GRATTAN ST.
BUILDING A                                                          Underground Car Park                                                                                                                                                                                                     348

a How long is the athletics track from end to end (not around)?
b What is the approximate area of the South Lawn?
c How far is it from Swanston Street down Monash Road (enter gate 4) to Wilson
Hall (building 151)?

SIMILARITY AND TRIGONOMETRY                                                                                                             289   CHAPTER 9
6 a Copy the shield onto the bottom left corner of a piece of square graph paper. Each
axis has a scale of 1 cm = 1 unit.
b Draw a new set of axes on the graph
page where the scale is 3 cm = 1 unit.
c Create an accurate enlargement of the        4
shield on the new set of axes.
d How many times larger is the                 3
enlargement?
2

1

0
1      2      3      4
7 a Repeat the steps in question 6 but change the horizontal scale on the enlargement
axes to 1 cm = 1 unit. Keep the vertical scale as 3 cm = 1 unit.
b Is the new enlargement mathematically similar to the original shield?

Wo rk in g m a th e m a tic a lly

Applying and v erifying
E nlarging a cartoon
1 Collect one cartoon character from your favourite cartoon.
2 Glue this onto grid paper.
3 Construct a set of axes around the character and rule a square grid over the top.
4 On a large piece of graph paper, draw a new set of axes with a larger scale on each axis.
5 Complete an accurate enlargement of your cartoon. Colour and display your ﬁnal piece
of work.

290         NELSON MATHS FOR WESTERN AUSTRALIA, BOOK 2

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