rotational symmetry power point

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    Symmetry

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    Line Symmetry

    Shape has line symmetry when one halfof it is the mirror image of the other half.

    Symmetry exists all around us and manypeople see it as being a thing ofbeauty.

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    Line Symmetry

    If a shape can be folded in half so that one

    half fits exactly on top of the other, then

    we say that the shape has got line

    symmetry.

    The fold is called a line of symmetry.

    This shape has got a vertical line of

    symmetry.

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    Line Symmetry in the Alphabet

    Which letters have got lines of symmetry?

    A B C D E F G H I

    J K L M N O P QRS T U V W X Y Z

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    Lines of Symmetry all around us

    Which of these road signs have got lines ofsymmetry?

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    Is a butterfly symmetrical?

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    Examples of line symmetry

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    Animals that have Line

    Symmetry

    Here are a few more great examples ofmirror image in the animal kingdom.

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    This photograph shows 2 lines of symmetry.One vertical, the other along the waterline.

    (Notice how the prayer towers, called minarets, are reflected in thewater and side to side).

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    Rotational Symmetry

    When a shape is rotated about its center,

    if it comes to rest in a position and looks

    exactly like the original, then it has

    rotational symmetry

    A shape like an equilateral triangle would

    have an order of rotational symmetry of 3

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    Rotational Symmetry

    The general rule for a regular polygon

    (shapes such as pentagons, heptagons,

    octagons etc.) is, that the number of sides

    is the same as the number of lines ofsymmetry, which is also the same as the

    rotational symmetry order.

    http://illuminations.nctm.org/imath/912/sy_rotations/page3.html

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    Rotational Symmetry If, when you rotate a shape, it looks

    exactly the same as it did in its original

    position, then we say that the shape has

    got rotational symmetry.

    This square has got rotationalsymmetry.

    It looks exactly the same four times in a

    full turn.

    It has got rotational symmetry order 4.

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    Rotational Symmetry

    Does this rectangle have rotationalsymmetry?

    It looks exactly the same twice in a full

    turn.

    It has got rotational symmetry order 2.

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    Rotational Symmetry in the

    AlphabetWhich letters have got rotational symmetry?

    A B C D E F G H I

    J K L M N O P QRS T U V W X Y Z

    Order 2 Order 2 Order 2

    Order 2 Order 2 Order 2

    Order 2

    R t ti l S t ll d

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    Rotational Symmetry all around

    us

    Order 3 Order 2 Order 2

    R t ti l S t ll d

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    Rotational Symmetry all around

    us

    Order 4 Order 3 Order 2

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    Plane Symmetry

    Plane symmetry concerns three-

    dimensional shapes or solids.

    Just as two-dimensional shapes can have

    a mirror line, so solid three-dimensional

    shapes can have a plane of symmetry.

    The symmetry planes of an object are

    imaginary mirrors in which it can be

    reflected while appearing unchanged

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    Plane Symmetry

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    Plane Symmetry

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    Plane Symmetry

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    Tesselation

    A collection of shapes that fit together to

    cover a surface without overlapping or

    leaving gaps

    May also be referred to as tiling

    They can be regular or irregular

    a regular tessellation is made up ofcongruent regular polygons - triangles,

    squares or hexagons

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    Tiling with regular polygon

    The only regular polygons that can tile the plane are:

    Equilateral Triangle

    Square

    Hexagon

    and no more!!

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    Pentagon

    Regular heptagon and those with more sides

    Whats wrong withthe other regular

    polygons??

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    Tesselation

    Can be an irregular tesselation