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Symmetry

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Symmetry Line Symmetry Shape has line symmetry when one half of it is the mirror image of the other half. Line Symmetry If a shape can be folded in half so that one ... – PowerPoint PPT presentation

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Title: Symmetry


1
Symmetry
2
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.

3
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.


4
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
5
Lines of Symmetry all around us
  • Which of these road signs have got lines of
    symmetry?

6
Is a butterfly symmetrical?
7
Examples of line symmetry
8
Animals that have Line Symmetry
  • Here are a few more great examples of mirror
    image in the animal kingdom.

9
  • 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).

10
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

11
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
12
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.

13
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.

14
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
15
Rotational Symmetry all around us
Order 3
Order 2
Order 2
16
Rotational Symmetry all around us
Order 4
Order 3
Order 2
17
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

18
Plane Symmetry
19
Plane Symmetry
20
Plane Symmetry
21
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

22
Tiling with regular polygon
  • The only regular polygons that can tile the plane
    are
  • Equilateral Triangle
  • Square
  • Hexagon
  • and no more!!

23
Whats wrong with the other regular polygons??
Pentagon
Regular heptagon and those with more sides
24
Tesselation
  • Can be an irregular tesselation
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