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Symmetry

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.

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Symmetry

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  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_rotations/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 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

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