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 therotational 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 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

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!!

Pentagon

Regular heptagon and those with more sides

What’s wrong with the other regular

polygons??

Tesselation

• Can be an irregular tesselation