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

Polygons with a ruler and a protractor 0 1 2 3 4 5 6

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 © T Madas

Drawing a Hexagon using a protractor © T Madas

Drawing a Hexagon using a protractor © T Madas

Drawing a Hexagon using a protractor A hexagon has 6 sides We are going

Drawing a Hexagon using a protractor 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? © T Madas

Drawing a Hexagon using a protractor • Start by drawing a circle. • The

Drawing a Hexagon using a protractor • 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 0 1 2 3 4 5 6 7 8 9 10 11 12 © T Madas 1

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0 80 10 110 70 120 0 13 60 14 15 0 0 160 170 180 30 20 10 0 50 40 80 1 00 70 110 60 50 12 13 0 0 Drawing a Hexagon using a protractor 90 0 4 1 50 0 1 4 0 3 160 20 0 10 17 0 180 Line up the dot & line © T Madas

80 100 70 0 11 60 0 50 2 1 0 13 100 80

80 100 70 0 11 60 0 50 2 1 0 13 100 80 11 1 0 70 1 20 3 60 0 90 1 4 0 15 0 40 30 1 6 0 2 170 1 0 0 180 0 50 © T Madas 40 0 30 14 50 1 20 160 0 170 1 180 0 Drawing a Hexagon using a protractor

Drawing a Hexagon using a protractor 0 1 2 3 4 5 6 7

Drawing a Hexagon using a protractor 0 1 2 3 4 5 6 7 8 9 10 11 12 © T Madas 1

12 0 1 2 3 4 5 6 7 8 9 10 11 Drawing

12 0 1 2 3 4 5 6 7 8 9 10 11 Drawing a Hexagon using a protractor © T Madas

11 0 1 2 3 4 5 6 7 8 9 10 Drawing a

11 0 1 2 3 4 5 6 7 8 9 10 Drawing a Hexagon using a protractor © T Madas

Drawing a Hexagon using a protractor 0 © T Madas 1 2 3 4

Drawing a Hexagon using a protractor 0 © T Madas 1 2 3 4 5 6 7 8 9 10 11 12 1

Drawing a Hexagon using a protractor 0 1 2 3 4 5 6 7

Drawing a Hexagon using a protractor 0 1 2 3 4 5 6 7 8 9 10 © T Madas 1

Drawing a Hexagon using a protractor 0 1 2 3 4 5 6 7

Drawing a Hexagon using a protractor 0 1 2 3 4 5 6 7 8 9 © T Madas

Drawing a Hexagon using a protractor © T Madas

Drawing a Hexagon using a protractor © T Madas

60° ° 60 60 ° 8 cm ° m 8 c m 60° °

60° ° 60 60 ° 8 cm ° m 8 c m 60° ° 60 8 c 8 cm 60 8 c m Drawing a Hexagon using a protractor © T Madas

Drawing an Octagon using a protractor © T Madas

Drawing an Octagon using a protractor © T Madas

Drawing an Octagon using a protractor An Octagon has 8 sides We are going

Drawing an Octagon using a protractor 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? © T Madas

Drawing an Octagon using a protractor • Start by drawing a circle. • The

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 0 1 2 3 4 5 6 7 8 9 10 11 12 © T Madas 1

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0 80 10 110 70 120 0 13 60 14 15 0 0 160 170 180 30 20 10 0 50 40 80 1 00 70 110 60 50 12 13 0 0 Drawing an Octagon using a protractor 90 0 4 1 50 0 1 4 0 3 160 20 0 10 17 0 180 Line up the dot & line © T Madas

80 100 70 0 11 60 0 50 2 1 0 13 100 80

80 100 70 0 11 60 0 50 2 1 0 13 100 80 11 1 0 70 1 20 3 60 0 90 1 4 0 15 0 40 30 1 6 0 2 170 1 0 0 180 0 50 © T Madas 40 0 30 14 50 1 20 160 0 170 1 180 0 Drawing an Octagon using a protractor

Drawing an Octagon using a protractor 0 1 2 3 4 5 6 7

Drawing an Octagon using a protractor 0 1 2 3 4 5 6 7 8 9 10 11 12 © T Madas 1

15 14 0 1 2 3 4 5 6 7 8 9 10 11

15 14 0 1 2 3 4 5 6 7 8 9 10 11 12 13 Drawing an Octagon using a protractor © T Madas

10 0 1 2 3 4 5 6 7 8 9 Drawing an Octagon

10 0 1 2 3 4 5 6 7 8 9 Drawing an Octagon using a protractor © T Madas

12 13 0 1 2 3 4 5 6 7 8 9 10 11

12 13 0 1 2 3 4 5 6 7 8 9 10 11 Drawing an Octagon using a protractor © T Madas

Drawing an Octagon using a protractor 0 © T Madas 1 2 3 4

Drawing an Octagon using a protractor 0 © T Madas 1 2 3 4 5 6 7 8 9 10 11 12

Drawing an Octagon using a protractor 0 1 2 3 4 5 6 7

Drawing an Octagon using a protractor 0 1 2 3 4 5 6 7 8 9 10 11 12 13 © T Madas

Drawing an Octagon using a protractor 0 1 2 3 4 5 6 7

Drawing an Octagon using a protractor 0 1 2 3 4 5 6 7 8 © T Madas 9

Drawing an Octagon using a protractor 0 1 2 3 4 5 6 7

Drawing an Octagon using a protractor 0 1 2 3 4 5 6 7 8 9 10 11 © T Madas

Drawing an Octagon using a protractor © T Madas

Drawing an Octagon using a protractor © T Madas

45° cm 6 6 45° 45° 6 cm cm 6 6 cm Drawing an

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

Drawing a Pentagon using a protractor © T Madas

Drawing a Pentagon using a protractor © T Madas

Drawing a Pentagon using a protractor A pentagon has 5 sides We are going

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? © T Madas

Drawing a Pentagon using a protractor • Start by drawing a circle. • The

Drawing a Pentagon using a protractor • 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 0 1 2 3 4 5 6 7 8 9 10 11 12 © T Madas 1

0 80 10 110 70 120 0 13 60 14 15 0 0 160

0 80 10 110 70 120 0 13 60 14 15 0 0 160 170 180 30 20 10 0 50 40 80 1 00 70 110 60 50 12 13 0 0 Drawing a Pentagon using a protractor 90 0 4 1 50 0 1 4 0 3 160 20 0 10 17 0 180 Line up the dot & line © T Madas

80 100 70 0 11 60 0 50 2 1 0 13 100 80

80 100 70 0 11 60 0 50 2 1 0 13 100 80 11 1 0 70 1 20 3 60 0 90 1 4 0 15 0 40 30 1 6 0 2 170 1 0 0 180 0 50 © T Madas 40 0 30 14 50 1 20 160 0 170 1 180 0 Drawing a Pentagon using a protractor

Drawing a Pentagon using a protractor 0 1 2 3 4 5 6 7

Drawing a Pentagon using a protractor 0 1 2 3 4 5 6 7 8 9 10 11 12 © T Madas 1

11 0 1 2 3 4 5 6 7 8 9 10 Drawing a

11 0 1 2 3 4 5 6 7 8 9 10 Drawing a Pentagon using a protractor © T Madas

Drawing a Pentagon using a protractor 7 6 5 0 © T Madas 1

Drawing a Pentagon using a protractor 7 6 5 0 © T Madas 1 2 3 4 8 9 10 11 12 13 14 15 16

Drawing a Pentagon using a protractor 0 1 2 3 4 5 6 7

Drawing a Pentagon using a protractor 0 1 2 3 4 5 6 7 © T Madas 8 9 10 11 12 13 14 15

Drawing a Pentagon using a protractor 0 1 2 3 4 5 6 7

Drawing a Pentagon using a protractor 0 1 2 3 4 5 6 7 8 9 © T Madas

Drawing a Pentagon using a protractor © T Madas

Drawing a Pentagon using a protractor © T Madas

cm 72 ° ° 2 7 72 8 cm ° 72 8 8 cm

cm 72 ° ° 2 7 72 8 cm ° 72 8 8 cm Drawing a Pentagon using a protractor © T Madas

Drawing an Enneagon using a protractor © T Madas

Drawing an Enneagon using a protractor © T Madas

Drawing an Enneagon using a protractor An Enneagon has 9 sides [It is also

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? © T Madas

Drawing an Enneagon using a protractor • Start by drawing a circle. • The

Drawing an Enneagon using a protractor • 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 0 1 2 3 4 5 6 7 8 9 10 11 12 © T Madas 1

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0 80 10 110 70 120 0 13 60 14 15 0 0 160 170 180 30 20 10 0 50 40 80 1 00 70 110 60 50 12 13 0 0 Drawing an Enneagon using a protractor 90 0 4 1 50 0 1 4 0 3 160 20 0 10 17 0 180 Line up the dot & line © T Madas

80 100 70 0 11 60 0 50 2 1 0 13 100 80

80 100 70 0 11 60 0 50 2 1 0 13 100 80 11 1 0 70 1 20 3 60 0 90 1 4 0 15 0 40 30 1 6 0 2 170 1 0 0 180 0 50 © T Madas 40 0 30 14 50 1 20 160 0 170 1 180 0 Drawing an Enneagon using a protractor

Drawing an Enneagon using a protractor 0 1 2 3 4 5 6 7

Drawing an Enneagon using a protractor 0 1 2 3 4 5 6 7 8 9 10 11 12 © T Madas 1

Drawing an Enneagon using a protractor 9 7 10 11 12 13 14 15

Drawing an Enneagon using a protractor 9 7 10 11 12 13 14 15 8 6 5 4 3 2 0 1 © T Madas 1

10 0 1 2 3 4 5 6 7 8 9 Drawing an Enneagon

10 0 1 2 3 4 5 6 7 8 9 Drawing an Enneagon using a protractor © T Madas

11 0 1 2 3 4 5 6 7 8 9 10 Drawing an

11 0 1 2 3 4 5 6 7 8 9 10 Drawing an Enneagon using a protractor © T Madas

Drawing an Enneagon using a protractor 0 © T Madas 1 2 3 4

Drawing an Enneagon using a protractor 0 © T Madas 1 2 3 4 5 6 7 8 9 10 11 12 13 1

Drawing an Enneagon using a protractor 0 © T Madas 1 2 3 4

Drawing an Enneagon using a protractor 0 © T Madas 1 2 3 4 5 6 7 8 9 10 11 12 13

Drawing an Enneagon using a protractor 0 1 2 3 4 5 6 7

Drawing an Enneagon using a protractor 0 1 2 3 4 5 6 7 8 9 10 1 © T Madas

Drawing an Enneagon using a protractor 0 1 2 3 4 5 6 7

Drawing an Enneagon using a protractor 0 1 2 3 4 5 6 7 8 © T Madas 9

Drawing an Enneagon using a protractor 0 1 2 3 4 5 6 7

Drawing an Enneagon using a protractor 0 1 2 3 4 5 6 7 8 9 10 11 12 © T Madas

Drawing an Enneagon using a protractor © T Madas

Drawing an Enneagon using a protractor © T Madas

40° m 7 cm 7 c 7 40° ° 40 ° 0 4 7

40° m 7 cm 7 c 7 40° ° 40 ° 0 4 7 cm ° 40° 7 cm 4 0° cm 40 m 7 c 7 cm Drawing an Enneagon using a protractor © T Madas

Polygons with Compasses and Straightedge 0 1 2 3 4 5 6 7 8

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 © T Madas

Constructing Regular Hexagons © T Madas

Constructing Regular Hexagons © T Madas

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

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

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

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

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

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

Constructing Regular Pentagons © T Madas

Constructing Regular Pentagons © T Madas

Constructing a Regular Pentagon • Start with the circumscribing circle • Draw a diameter

Constructing a Regular Pentagon • 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 © T Madas

Constructing Regular Octagons © T Madas

Constructing Regular Octagons © T Madas

Constructing a Regular Octagon © T Madas

Constructing a Regular Octagon © T Madas

Constructing Regular Decagons © T Madas

Constructing Regular Decagons © T Madas

Constructing a Regular Decagon • To construct a decagon you need a regular pentagon

Constructing a Regular Decagon • 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 © T Madas

© T Madas

© T Madas