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# Symmetry

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### Symmetry

1. 1.  Fundamental organizing principle in nature and art.  Preserves distances, angles, sizes and shapes.
2. 2.  Line symmetry  line that divides a figure into two halves that are mirror images of each other
3. 3.  An attribute of a shape  exact reflection of form on opposite sides of a dividing line  Line symmetry  line that divides a figure into two halves that are mirror images of each other
4. 4.  Sort the letters of the alphabet into groups according to their symmetries  Divide letters into two categories:  symmetrical  not symmetrical
5. 5. A B C D E H I M O T U V W X Y There are some letters which do not have any line of symmetry. F G J K L N P Q S Z
6. 6. Letters and Rotational N S X I O Z rotational symmetry at order 1 rotational symmetry at order 2 rotational symmetry at order 2 rotational symmetry at order 2 rotational symmetry at order 2 rotational symmetry at order 2 rotational symmetry at order 1 Symmetry.
7. 7.  An image has Rotational Symmetry if there is a center point around which the object is turned a certain number of degrees and the object still looks the same. an equilateral triangle has 3 internal angles,3 lines of symmetry & a rotational symmetry at order 3. a square has 4 internal angles, 4 lines of symmetry a rotational symmetry at order 4. A regular pentagon has 5 internal angles,5 lines of symmetry & a rotational symmetry at order 5. a regular octagon has 8 internal angles,8 lines of symmetry & a rotational symmetry at order 8. A shape has line symmetry when one half of it is the mirror image of the other half.
8. 8. Common Errors  There are some examples of shapes that are tricky when considering symmetry. A typical parallelogram actually cannot be folded in half even though it appears to have two 'equal halves'. • We can see both kinds of symmetry around us; rotational as well as line symmetry.
9. 9. Order 3+0 lines of symmetry. Order 2+1 line of symmetry. Order 4+4 lines of symmetry Order 3+0 line of symmetry. Order 2+0 line of symmetry. Order 1+1 line of symmetry.
10. 10. Symmetry exists in architecture all around the world. One of the best known examples of this is the Taj Mahal. If an object is reflected in water many people believe the image has line symmetry. But is it really a 'mirror image'? Is it really symmetrical? What are your thoughts? The image can be rotational symmetry.
11. 11. Japan Indonesia Micronesia United Nations Aboriginal Flag of Australia Finland Canada British
12. 12. Rotational symmetry-yes( 2) Rotational symmetry-yes( 2) Rotational symmetry-yes( 1) Rotational symmetry-yes( 1) Rotational symmetry-yes( 1) Rotational symmetry-yes( 2) Rotational symmetry-yes( 1) Rotational symmetry-yes( 1)
13. 13.  Click on the shapes to see how many lines of symmetry they have.