1. © T Madas 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

2. © T Madas Polygons with a ruler and a protractor 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

3. © T Madas Drawing a Hexagon using a protractor

4. © T Madas A hexagon has 6 sides We are going to construct 6 equal angles around a point How many degrees are there around a point? How many degrees each of these angles must be? Drawing a Hexagon using a protractor

5. © T Madas Drawing a Hexagon using a protractor 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Start by drawing a circle. The hexagon will be inscribed in the circle. The bigger the circle the bigger the hexagon Mark a horizontal line from the centre

6. © T Madas 180 10 20 170 0 160 30 150 40 140 50 130 60 120 70 110 80 100 90 180 170 160 140 150 130 120 110 100 80 70 60 50 40 30 20 10 0 Line up the dot & line Drawing a Hexagon using a protractor

7. © T Madas 180 10 20 170 0 160 30 150 40 140 50 130 60 120 70 110 80 100 90 180 170 160 140 150 130 120 110 100 80 70 60 50 40 30 20 10 0 Drawing a Hexagon using a protractor

8. © T Madas 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Drawing a Hexagon using a protractor

9. © T Madas Drawing a Hexagon using a protractor 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

10. © T Madas Drawing a Hexagon using a protractor 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

11. © T Madas 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Drawing a Hexagon using a protractor

12. © T Madas 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Drawing a Hexagon using a protractor

13. © T Madas 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Drawing a Hexagon using a protractor

14. © T Madas Drawing a Hexagon using a protractor

15. © T Madas 60° 8 cm Drawing a Hexagon using a protractor

16. © T Madas Drawing an Octagon using a protractor

17. © T Madas An Octagon has 8 sides We are going to construct 8 equal angles around a point How many degrees are there around a point? How many degrees each of these angles must be? Drawing an Octagon using a protractor

18. © T Madas 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Drawing an Octagon using a protractor Start by drawing a circle. The octagon will be inscribed in the circle. The bigger the circle the bigger the octagon Mark a horizontal line from the centre

19. © T Madas 180 10 20 170 0 160 30 150 40 140 50 130 60 120 70 110 80 100 90 180 170 160 140 150 130 120 110 100 80 70 60 50 40 30 20 10 0 Line up the dot & line Drawing an Octagon using a protractor

20. © T Madas 180 10 20 170 0 160 30 150 40 140 50 130 60 120 70 110 80 100 90 180 170 160 140 150 130 120 110 100 80 70 60 50 40 30 20 10 0 Drawing an Octagon using a protractor

21. © T Madas 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Drawing an Octagon using a protractor

22. © T Madas Drawing an Octagon using a protractor 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

23. © T Madas Drawing an Octagon using a protractor 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

24. © T Madas Drawing an Octagon using a protractor 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

25. © T Madas 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Drawing an Octagon using a protractor

26. © T Madas 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Drawing an Octagon using a protractor

27. © T Madas 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Drawing an Octagon using a protractor

28. © T Madas 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Drawing an Octagon using a protractor

29. © T Madas Drawing an Octagon using a protractor

30. © T Madas 6 cm 45° Drawing an Octagon using a protractor

31. © T Madas Drawing a Pentagon using a protractor

32. © T Madas Drawing a Pentagon using a protractor A pentagon has 5 sides We are going to construct 5 equal angles around a point How many degrees are there around a point? How many degrees each of these angles must be?

33. © T Madas Drawing a Pentagon using a protractor 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Start by drawing a circle. The pentagon will be inscribed in the circle. The bigger the circle the bigger the pentagon Mark a horizontal line from the centre

34. © T Madas Drawing a Pentagon using a protractor 180 10 20 170 0 160 30 150 40 140 50 130 60 120 70 110 80 100 90 180 170 160 140 150 130 120 110 100 80 70 60 50 40 30 20 10 0 Line up the dot & line

35. © T Madas Drawing a Pentagon using a protractor 180 10 20 170 0 160 30 150 40 140 50 130 60 120 70 110 80 100 90 180 170 160 140 150 130 120 110 100 80 70 60 50 40 30 20 10 0

36. © T Madas Drawing a Pentagon using a protractor 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

37. © T Madas Drawing a Pentagon using a protractor 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

38. © T Madas Drawing a Pentagon using a protractor 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

39. © T Madas Drawing a Pentagon using a protractor 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

40. © T Madas Drawing a Pentagon using a protractor 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

41. © T Madas Drawing a Pentagon using a protractor

42. © T Madas Drawing a Pentagon using a protractor 72° 8 cm

43. © T Madas Drawing an Enneagon using a protractor

44. © T Madas Drawing an Enneagon using a protractor An Enneagon has 9 sides [It is also called a nonagon but enneagon is its proper name] We are going to construct 9 equal angles around a point How many degrees are there around a point? How many degrees each of these angles must be?

45. © T Madas Drawing an Enneagon using a protractor 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Start by drawing a circle. The enneagon will be inscribed in the circle. The bigger the circle the bigger the enneagon Mark a horizontal line from the centre

46. © T Madas Drawing an Enneagon using a protractor 180 10 20 170 0 160 30 150 40 140 50 130 60 120 70 110 80 100 90 180 170 160 140 150 130 120 110 100 80 70 60 50 40 30 20 10 0 Line up the dot & line

47. © T Madas Drawing an Enneagon using a protractor 180 10 20 170 0 160 30 150 40 140 50 130 60 120 70 110 80 100 90 180 170 160 140 150 130 120 110 100 80 70 60 50 40 30 20 10 0

48. © T Madas Drawing an Enneagon using a protractor 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

49. © T Madas Drawing an Enneagon using a protractor 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

50. © T Madas Drawing an Enneagon using a protractor 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

51. © T Madas Drawing an Enneagon using a protractor 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

52. © T Madas Drawing an Enneagon using a protractor 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

53. © T Madas Drawing an Enneagon using a protractor 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

54. © T Madas Drawing an Enneagon using a protractor 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

55. © T Madas Drawing an Enneagon using a protractor 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

56. © T Madas Drawing an Enneagon using a protractor 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

57. © T Madas Drawing an Enneagon using a protractor

58. © T Madas Drawing an Enneagon using a protractor 40° 7 cm

59. © T Madas Polygons with Compasses and Straightedge 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

60. © T Madas Constructing Regular Hexagons

61. Constructing a Regular Hexagon Why does it work?

62. © T Madas Constructing a Regular Hexagon Why does it work?

63. © T Madas Constructing a Regular Hexagon Why does it work?

64. © T Madas Constructing Regular Pentagons

65. Start with the circumscribing circle Draw a diameter Draw the perpendicular bisector of that diameter Mark its intersection with the circle Bisect the radius as shown Draw arc as shown and mark its intersection with the diameter This is the required side length for a regular pentagon, which is circumscribed by the circle Constructing a Regular Pentagon

66. © T Madas Constructing Regular Octagons

67. Constructing a Regular Octagon

68. Constructing Regular Decagons

69. To construct a decagon you need a regular pentagon first Bisect one of the sides of the pentagon Use the chord of the new arc produced to construct a regular decagon You can use this idea to constuct a dodecagon from a hexagon A 16 – sided regular polygon using an octagon An eicosagon from a decagon and so on Constructing a Regular Decagon

70. © T Madas