Similar Shapes With Examples Pp t

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    Similar Figures

    (Not exactly the same,

    but pretty close!)

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    Lets do a little

    review work

    before discussing

    similar figures.

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    Congruent Figures

    In order to be congruent, two

    figures must be the same sizeand same shape.

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    Similar Figures

    Similar figures must be the

    same shape, but their sizes maybe different.

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    Similar Figures

    This is the symbol that

    means similar.

    These figures are the same

    shape but different sizes.

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    SIZES

    Although the size of the twoshapes can be different, the

    sizes of the two shapes mustdiffer by a factor.

    3 3

    2

    1

    6 6

    2

    4

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    SIZES

    In this case, the factor is x 2.

    3 3

    2

    1

    6 6

    2

    4

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    SIZES

    Or you can think of the factoras 2.

    3 3

    2

    1

    6 6

    2

    4

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    Enlargements

    When you have a photographenlarged, you make a similar

    photograph.

    X 3

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    Reductions A photograph can also be

    shrunk to produce a slide.

    4

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    Determine the length of the

    unknown side.

    12

    9

    15

    4

    3

    ?

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    These triangles differ by a factor

    of 3.

    12

    9

    15

    4

    3

    ?

    15 3= 5

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    Determine the length of the

    unknown side.

    4

    2

    24

    ?

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    These dodecagons differ by a

    factor of 6.

    4

    2

    24

    ?

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    Sometimes the factor between 2

    figures is not obvious and some

    calculations are necessary.

    18

    12 15

    12

    108

    ? =

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    To find this missing factor,

    divide 18 by 12.

    18

    12 15

    12

    108

    ? =

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    18 divided by 12

    = 1.5

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    The value of the missing

    factor is 1.5.

    18

    12 15

    12

    108

    1.5 =

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    When changing the size of a

    figure, will the angles of the

    figure also change?

    ? ?

    ?

    7070

    40

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    Nope! Remember, the sum of all 3

    angles in a triangle MUST add to 180

    degrees.If the size of the

    angles were

    increased,the sum

    would exceed

    180

    degrees.

    70 70

    40

    7070

    40

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    70 70

    40

    We can verify this fact by placing

    the smaller triangle inside the

    larger triangle.

    7070

    40

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    70 70

    70 70

    40

    The 40 degree angles

    are congruent.

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    70 707070

    70

    40

    40

    The 70 degree angles

    are congruent.

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    70 707070

    70

    40

    4

    The other 70 degree

    angles are congruent.

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    Find the length of the missing

    side.

    30

    40

    50

    6

    8

    ?

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    This looks messy. Lets

    translate the two triangles.

    30

    40

    50

    6

    8

    ?

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    Now things are easier to see.

    30

    40

    50

    8

    ?

    6

    Th f t b t

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    The common factor between

    these triangles

    is 5.

    30

    40

    50

    8

    ?

    6

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    So the length of

    the missing side

    is?

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    Thats right! Its ten!

    30

    40

    50

    8

    10

    6

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    Similarity is used to answer real

    life questions. Suppose that you

    wanted to find theheight of this tree.

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    Unfortunately all that

    you have is a tapemeasure, and you are

    too short to reach the

    top of the tree.

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    You can measure the length of

    the trees shadow.

    10 feet

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    Then, measure the length of your

    shadow.

    10 feet 2 feet

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    The tree must be 30 ft tall. Boy,

    thats a tall tree!

    10 feet 2 feet6 ft

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    Similar figures work just like

    equivalent fractions.

    530

    66 11

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    These numerators and

    denominators differ by a factor of

    6.

    530

    66 11

    6

    6

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    Two equivalent fractions are

    called a proportion.

    530

    66 11

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    Similar Figures

    So, similar figures are

    two figures that are thesame shape and whose

    sides are proportional.

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    Practice Time!

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    1) Determine the missing side of

    the triangle.

    3

    4

    5

    12

    9

    ?

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    1) Determine the missing side of

    the triangle.

    3

    4

    5

    12

    9

    15

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    2) Determine the missing side of

    the triangle.

    6

    4

    6 36 36

    ?

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    2) Determine the missing side of

    the triangle.

    6

    4

    6 36 36

    24

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    3) Determine the missing sides of

    the triangle.

    39

    24

    33?

    8

    ?

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    3) Determine the missing sides of

    the triangle.

    39

    24

    3313

    8

    11

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    4) Determine the height of the

    lighthouse.

    2.5

    8

    10

    ?

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    4) Determine the height of the

    lighthouse.

    2.5

    8

    10

    32

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    5) Determine the height of the

    car.

    5

    3

    12

    ?

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    5) Determine the height of the

    car.

    5

    3

    12

    7.2

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    THE END!