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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
                                                                                                                                                                                                                                                                                                                                                                                                Spencer Road




                                                                                         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
                                                                                                                                                                                                                                                                Administration                                                                                        133                                                                  GALLERY
                                                                                                                                                                                                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


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




                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     FARADAY S
                                                                                                                                                                                                                                                   WILSON




                                                                                         194                                                                                                                                                                                                                                                                                              156
                                                                                                                                                                                                                                                    HALL




                                                                                                                                                                                                                                                                                                                                                                                                       Monash         Road
                         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
                    PARADE




                                                                                                                            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
                                                                                                                                                                                                                           Kernot Road                                                                                                                                                                          GRADUATE CENTRE
                                                                                                                                                                                                                                                                                                                                                                                                                                              CENTRE




                                                                                                                           ADMIN.
                                                                                                                                                                                                                                                                                                                                                                                                                 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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