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Rotational and Reflectional Symmetry

This resource provides a comprehensive overview of rotational and reflectional symmetry in two-dimensional shapes. Learn about the concept of rotational symmetry and the different orders (Order 1, 2, 3, 4) associated with various geometric figures like triangles, squares, and pentagons. Explore how to identify the order of symmetry by determining how many times a shape fits onto itself during a full rotation. Additionally, the document covers reflectional symmetry, explaining how specific shapes can be folded along lines of reflection to mirror themselves.

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Rotational and Reflectional Symmetry

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  1. Rotational and Reflectional Symmetry Oct. 2, 2018

  2. Order 4 Order 2 Order 1 Order 3 Rotational Symmetry All 2 dimensional shapes have some rotational symmetry. The degree of rotational symmetry that an object has is known as its order. For shapes that have “order 2” rotational symmetry or higher, a single centre of rotation can be located. For shapes that have only “order 1” rotational symmetry a centre of rotation can be found anywhere within it. The order of rotational symmetry that an object has is the number of times that it fits on to itself during a full rotation of 360 degrees.

  3. Rotational Symmetry The order of rotational symmetry that an object has is the number of times that it fits on to itself during a full rotation of 360 degrees. Order 1

  4. Rotational Symmetry The order of rotational symmetry that an object has is the number of times that it fits on to itself during a full rotation of 360 degrees. 2 1 Order 2 Order 1

  5. Rotational Symmetry The order of rotational symmetry that an object has is the number of times that it fits on to itself during a full rotation of 360 degrees. 2 1 Order 2 Order 1 3 2 1 Order 3

  6. Rotational Symmetry The order of rotational symmetry that an object has is the number of times that it fits on to itself during a full rotation of 360 degrees. 2 1 Order 2 Order 1 3 3 4 2 1 1 2 Order 4 Order 3

  7. Rotational Symmetry What is the order of rotational symmetry of the shape below?

  8. Rotational Symmetry What is the order of rotational symmetry of the shape below? 5 4 1 2 3 Order 5

  9. Rotational Symmetry What is the order of rotational symmetry of the shape below?

  10. Rotational Symmetry What is the order of rotational symmetry of the shape below? 6 5 1 2 4 3 Order 6

  11. Regular Polygons Equilateral Triangle An equilateral triangle has rotational symmetry of order ?

  12. Equilateral Triangle An equilateral triangle has rotational symmetry of order ?

  13. Equilateral Triangle 3 An equilateral triangle has rotational symmetry of order ? 3 2 1

  14. Square Square A square has rotational symmetry of order ?

  15. Square A square has rotational symmetry of order ?

  16. Square 4 A square has rotational symmetry of order ? 3 4 2 1

  17. Pentagon Regular Pentagon A regular pentagon has rotational symmetry of order ?

  18. Regular Pentagon A regular pentagon has rotational symmetry of order ?

  19. Regular Pentagon 5 A regular pentagon has rotational symmetry of order ? 5 4 1 2 3

  20. Hexagon Regular Hexagon A regular hexagon has rotational symmetry of order ?

  21. Regular Hexagon A regular hexagon has rotational symmetry of order ?

  22. Regular Hexagon 6 A regular hexagon has rotational symmetry of order ? 5 6 1 4 2 3

  23. Octagon Regular Octagon A regular octagon has rotational symmetry of order ?

  24. Regular Octagon 8 A regular octagon has rotational symmetry of order ? 7 8 6 1 5 2 3 4

  25. Rectangle Rectangle A rectangle has rotational symmetry of order ?

  26. Rectangle 2 A rectangle has rotational symmetry of order ? 2 1

  27. Parallelogram A parallelogram has rotational symmetry of order ? Parallelogram

  28. Parallelogram 2 A parallelogram has rotational symmetry of order ? 2 1

  29. Isosceles Triangle An isosceles triangle has rotational symmetry of order ? Isos Tri

  30. Isosceles Triangle 1 An isosceles triangle has rotational symmetry of order ? 1 Isos Tri

  31. Scalene Triangle An scalene triangle has rotational symmetry of order ? Scalene Tri

  32. Scalene Triangle 1 An scalene triangle has rotational symmetry of order ? 1

  33. Isosceles Trapezium An isosceles trapezium has rotational symmetry of order ? Isos Trapezium

  34. Isosceles Trapezium 1 An isosceles trapezium has rotational symmetry of order ? 1

  35. Trapezium A trapezium has rotational symmetry of order ? Trapezium

  36. Trapezium 1 A trapezium has rotational symmetry of order ? 1

  37. Kite A kite has rotational symmetry of order ? Kite

  38. Kite 1 A kite has rotational symmetry of order ? 1

  39. Rhombus A rhombus has rotational symmetry of order ? Rhombus

  40. Rhombus 2 A rhombus has rotational symmetry of order ? 2 1

  41. Ellipse An ellipse has rotational symmetry of order ? Ellipse

  42. Ellipse 2 An ellipse has rotational symmetry of order ? Ellipse 2 1

  43. Rotational Symmetry State the order of rotational symmetry for each shape below: 1 2 3 4 Questions 1 Order 2 Order 3 Order 6 Order 2 7 5 8 6 Order 5 Order 2 Order 3 Order 1 10 9 11 12 Order 4 Order 1 Order 6 Order 8

  44. Rotational Symmetry State the order of rotational symmetry for each shape below: 1 2 3 4 Worksheet 1 7 5 8 6 9 10 11 12

  45. Rotational Symmetry State the order of rotational symmetry for each shape below: 13 14 15 16 Questions 2 Order 5 Order 2 Order 4 Order 1 19 17 20 18 Order 3 Order 6 Order 4 Order 2 22 21 23 24 Order 5 Order 4 Order 3 Order 1

  46. Rotational Symmetry State the order of rotational symmetry for each shape below: 13 14 15 16 Worksheet 2 19 17 20 18 21 22 23 24

  47. REFLECTION Sometimes, a figure has reflectional symmetry. This means that it can be folded along a line of reflection within itself so that the two halves of the figure match exactly, point by point. Basically, if you can fold a shape in half and it matches up exactly, it has reflectional symmetry.

  48. REFLECTIONAL SYMMETRY An easy way to understand reflectional symmetry is to think about folding. Do you remember folding a piece of paper, drawing half of a heart, and then cutting it out? What happens when you unfold the piece of paper?

  49. REFLECTIONAL SYMMETRY Line of Symmetry Reflectional Symmetry means that a shape can be folded along a line of reflection so the two haves of the figure match exactly, point by point. The line of reflection in a figure with reflectional symmetry is called a line of symmetry. The two halves are exactly the same… They are symmetrical. The two halves make a whole heart.

  50. REFLECTIONAL SYMMETRY The line created by the fold is the line of symmetry. How can I fold this shape so that it matches exactly? A shape can have more than one line of symmetry. Where is the line of symmetry for this shape? I CAN THIS WAY NOT THIS WAY Line of Symmetry

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