Symmetry

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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 many people see
  it as being a thing of beauty.

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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
Q
R
S
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 of
  symmetry?

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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 of mirror
  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 the water and side to side).

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Rotational Symmetry

• When a shape is rotated about its centre, 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 of symmetry, which is also the
  same as therotational symmetry order.

http//illuminations.nctm.org/imath/912/sy_rotatio
ns/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 rotational symmetry.

• 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 rotational symmetry?

• 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 Alphabet

• Which letters have got rotational symmetry?

A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
Order 2
Order 2
Order 2
Order 2
S
T
U
V
W
X
Y
Z
Order 2
Order 2
Order 2
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Rotational Symmetry all around us
Order 3
Order 2
Order 2
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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 of congruent
  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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Whats wrong with the other regular polygons??
Pentagon
Regular heptagon and those with more sides
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Tesselation

• Can be an irregular tesselation