1. Symmetry

2. Line Symmetry
Shape has line symmetry when one half of it is the mirror image of the other half.
        How would you define the term 'line symmetry'?         Why might some people see line symmetry as a thing of beauty?
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
This type of symmetry is also called reflectional symmetry as the two parts reflect/match along each side of a dividing line ( or axis ).

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
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 the rotational symmetry order.

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
Order 2 K L
Order 2 M N
Order 2 O P
Order 2 Q R 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. What’s wrong with the other regular polygons??
Pentagon
Regular heptagon and those with more sides

24. Tesselation
Can be an irregular tesselation