6.1 Polygons - Line and Rotation Symmetry.pptx

Symmetry - polygons

1. 6.1 Polygons Line and Rotation Symmetry

2. Objectives: Identify, describe and sketch regular polygons, including reference to sides, angles and symmetrical properties. Identify reflective (line) symmetry and order of rotational symmetry of 2D shapes and patterns.

3. Simple Polygons or not ? What is a Polygon? Closed 2-dimensional shape All sides are simple All sides are straight lines

4. Can we name these polygons? (SB #P60- Q1 ) 5 min Equilateral Triangle Square Pentagon Hexagon Heptagon Octagon Nonagon Decagon Poly: many - g on : angle Tri: 3 Tetra: 4 Penta : 5 H exa : 6 Hepta : 7 Octa : 8 Nona: 9 Ennea : 9 Deca : 1o Hendeca : 11 Dodeca : 12 Trideca :

5. What Is a Quadrilateral? a 2D shape all of its sides are straight has 4 interior angles that add up to 360° a 4-sided shape

6. Parallelogram Do you know what are the properties of a parallelogram ? The diagonals of a parallelogram bisect each other In a rhombus, all of the sides are equal. It has 2 pairs of equal parallel sides. Opposite angles are equal. 2 angles are acute and 2 are obtuse. Every two adjacent angles add up to 180◦ (Co-interior angles)

7. Activity 1 Properties of Quadrilateral 1 -Distribute sheets A , B ,C,D for each group 2 –Write all about : 2.1 the sides 2.2 the angles 2.3 the diagonals 3- Present your work 8 Group T ime 4 mins + 2min for each group presentation T otal time 12 mins

8. Rectangle Do you know what are the properties of a rectangle? Opposite sides are parallel and of equal length. Every angle is a right angle (90°). Squares can be classified as rectangles, but not all rectangles can be classified as squares. Can you explain why? The diagonals of a rectangle are equal in length and bisect each other.

9. Kite Has 2 pairs of equal, adjacent sides. Diagonals of a kite are perpendicular. One diagonal bisects the other. 1 pair of opposite angle are equal. Do you know what the properties of a kite are?

10. Rhombus Do you know what are the properties of a rhombus? All 4 sides are of equal length. Opposite angles are equal. 2 angles are acute and 2 are obtuse. Opposite sides are parallel. Diagonals of a rhombus are perpendicular and bisect each other.

11. Square Do you know what are the properties of a square ? All sides are of equal length. Opposite sides are parallel. All interior angles are equal. The diagonals of the square are equal in length, perpendicular and bisect each other

12. Trapezium Do you know what the properties of a trapezium are? Has 1 pair of parallel sides. Right angled Trapezium Isosceles Trapezium Trapezium

13. What is a Regular Polygon ? Regular polygon when: All sides are equal in length, All angles are equal and

14. Regular / Irregular Polygons Which polygon is regular?      2 min Regular polygon : Equal sides and equal angles ( )

15. Tetragon They are polygons with 4 sides Which quadrilaterals are regular? 2 min Quadrilaterals

16. Reflective Symmetry – Line of Symmetry How many times can we fold the polygon in half such that the two halves exactly match? Fold “This is a line of symmetry because it splits the shape into two equal parts which are mirror images.”

17. What is the line of symmetry ?

18. How many lines of symmetry? There are 8 lines of symmetry.

19. How many lines of symmetry? The shape has five lines of symmetry.

20. Mirror Line – Line of Symmetry Reflective Symmetry Can you complete the symmetrical pattern? What is your strategy? Can you start closest to the mirror line? How can you check your answer? Can you see another line of symmetry? Repeat for other patterns.

21. What is the rotation of symmetry ?

22. Rotational Symmetry How many positions can we position the polygon to rotate one complete rotation such that each time will match the original shape?

23. Reflective symmetry or rotational symmetry? 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 . 360°

24. Activity 2 Lines of symmetry and rotational Symmetry for regular polygons 1- Distribute the regular polygons and the tracing sheets 2- How may times you can fold the shape 3 – State the number of lines of symmetry 4- Using the tracing paper rotate the shape 5 – State the order of rotation symmetry 5 min Pair Activity

25. What is the order of rotational symmetry?

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

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

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

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

30. Square A square has rotational symmetry of order ?

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

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

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

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

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

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

37. 1 2 3 4 5 6 Regular Hexagon A regular hexagon has rotational symmetry of order ? 6

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

39. 1 2 3 4 5 6 Regular Octagon A regular octagon has rotational symmetry of order ? 8 7 8

40. For Regular Polygons Number of sides Number of lines of symmetry Order of rotational symmetry Are all the same And more ………

41. 1 Order of rotational symmetry:

42. 1 Order of rotational symmetry: 2

43. 3 2 Order of rotational symmetry:

44. 3 4 Order of rotational symmetry:

45. Activity 3 Lines of symmetry and rotational Symmetry for irregular polygons 1- Distribute the irregular polygons and the tracing papers 2- How may times you can fold the shape 3 – State the number of lines of symmetry 4- Using the tracing paper rotate the shape 5 - State the order of rotation symmetry

46. 1 Order of rotational symmetry:

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

48. 2 1 2 Rectangle A rectangle has rotational symmetry of order ?

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

50. 2 1 2 Parallelogram A parallelogram has rotational symmetry of order ?

51. Why parallelogram has no line of symmetry? P arallelogram has no line of symmetry and 2 order of rotation symmetry.

52. Isosceles Triangle An isosceles triangle has rotational symmetry of order ?

53. 1 1 Isosceles Triangle An isosceles triangle has rotational symmetry of order ?

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

55. 1 1 Scalene Triangle An scalene triangle has rotational symmetry of order ?

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

57. 1 1 Isosceles Trapezium An isosceles trapezium has rotational symmetry of order ?

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

59. 1 1 A kite has rotational symmetry of order ? Kite

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

61. 2 1 A rhombus has rotational symmetry of order ? Rhombus 2

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

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

64. Activity 4 lines of symmetry and rotational symmetry for polygons 1- Distribute sheets 1.1 table 1 1.2 table 2 2 - Complete the tables 3- Check your work 5 min Pair Activity

65. 4 2 2 1 1 5 9 3 Group activity 3 min 4 2 2 1 1 1 5 6 3 4 2 2 1 1 5 9 3

66. Group discussion – Then solve o n your white board: 3 Octagon 4 5 Hexagon 3 5 min

67. Individual Activity – Complete the table ( S B # P62- Ex 2) 1 B C SHAPE Reflective Symmetry Rotational Symmetry A B C 5 min 5 5 2 2 1 1 Mark – Rotate – observe number of orders that fits exactly 2 3 4 5 1 2 1 A

68. Individual Activity (SB # P63 – Ex2 - Q1) Draw two quadrilaterals, both with two lines of symmetry, and rotational symmetry of order 2. Name the quadrilaterals. 10 min 10 min

69. CLASS WORK Student Book 7 Page 60 - 61 Exercise 1 Q 2, 3, 4 10min