Symmetry
Line Symmetry
• Shape has line symmetry when one half
of 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.
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.
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
Lines of Symmetry all around us
Which of these road signs have got lines of
symmetry?
Is a butterfly symmetrical?
Examples of line symmetry
Animals that have Line
Symmetry
Here are a few more great examples of
mirror image in the animal kingdom.
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).
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
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 the
rotational symmetry order.
http://illuminations.nctm.org/imath/912/sy_rotations/page3.html
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.
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.
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
S T U V W X Y Z
Order 2
Order 2
Order 2
Order 2
Order 2
Order 2
Order 2
Rotational Symmetry all around
us
Order 3
Order 2
Order 2
Rotational Symmetry all around
us
Order 4
Order 3
Order 2
Plane Symmetry
• Plane symmetry concerns threedimensional 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
Plane Symmetry
Plane Symmetry
Plane Symmetry
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
Tiling with regular polygon
The only regular polygons that can tile the plane are:
Equilateral Triangle
Square
Hexagon
… and no more!!
What’s wrong with
the other regular
polygons??
Pentagon
Regular heptagon and those with more sides
Tesselation
• Can be an irregular tesselation