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Transcript of © 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.
![Page 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.](https://reader035.fdocuments.us/reader035/viewer/2022062304/56649ea85503460f94bac1be/html5/thumbnails/1.jpg)
© T Madas
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© T Madas
Polygons with a ruler and a protractor0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
![Page 3: © 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.](https://reader035.fdocuments.us/reader035/viewer/2022062304/56649ea85503460f94bac1be/html5/thumbnails/3.jpg)
© T Madas
Drawing a Hexagon using a protractor
![Page 4: © 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.](https://reader035.fdocuments.us/reader035/viewer/2022062304/56649ea85503460f94bac1be/html5/thumbnails/4.jpg)
© T Madas
A hexagon has 6 sidesWe 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
![Page 5: © 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.](https://reader035.fdocuments.us/reader035/viewer/2022062304/56649ea85503460f94bac1be/html5/thumbnails/5.jpg)
© T Madas
Drawing a Hexagon using a protractor
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•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
![Page 6: © 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.](https://reader035.fdocuments.us/reader035/viewer/2022062304/56649ea85503460f94bac1be/html5/thumbnails/6.jpg)
© T Madas
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Line up the dot & line
Drawing a Hexagon using a protractor
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© T Madas
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Drawing a Hexagon using a protractor
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Drawing a Hexagon using a protractor
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© T Madas
Drawing a Hexagon using a protractor
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© T Madas
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Drawing a Hexagon using a protractor
![Page 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.](https://reader035.fdocuments.us/reader035/viewer/2022062304/56649ea85503460f94bac1be/html5/thumbnails/12.jpg)
© T Madas
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Drawing a Hexagon using a protractor
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Drawing a Hexagon using a protractor
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© T Madas
Drawing a Hexagon using a protractor
![Page 15: © 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.](https://reader035.fdocuments.us/reader035/viewer/2022062304/56649ea85503460f94bac1be/html5/thumbnails/15.jpg)
© T Madas
60°
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60°
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60°8 cm 8 cm
8 c
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8 cm
8 cm
Drawing a Hexagon using a protractor
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© T Madas
Drawing an Octagon using a protractor
![Page 17: © 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.](https://reader035.fdocuments.us/reader035/viewer/2022062304/56649ea85503460f94bac1be/html5/thumbnails/17.jpg)
© T Madas
An Octagon has 8 sidesWe 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
![Page 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.](https://reader035.fdocuments.us/reader035/viewer/2022062304/56649ea85503460f94bac1be/html5/thumbnails/18.jpg)
© 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
![Page 19: © 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.](https://reader035.fdocuments.us/reader035/viewer/2022062304/56649ea85503460f94bac1be/html5/thumbnails/19.jpg)
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Line up the dot & line
Drawing an Octagon using a protractor
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© T Madas
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Drawing an Octagon using a protractor
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© T Madas
Drawing an Octagon using a protractor
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© T Madas
Drawing an Octagon using a protractor
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© T Madas
Drawing an Octagon using a protractor
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© T Madas
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Drawing an Octagon using a protractor
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Drawing an Octagon using a protractor
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© T Madas
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Drawing an Octagon using a protractor
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© T Madas
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Drawing an Octagon using a protractor
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© T Madas
Drawing an Octagon using a protractor
![Page 30: © 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.](https://reader035.fdocuments.us/reader035/viewer/2022062304/56649ea85503460f94bac1be/html5/thumbnails/30.jpg)
© T Madas
6 cm
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Drawing an Octagon using a protractor
![Page 31: © 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.](https://reader035.fdocuments.us/reader035/viewer/2022062304/56649ea85503460f94bac1be/html5/thumbnails/31.jpg)
© T Madas
Drawing a Pentagon using a protractor
![Page 32: © 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.](https://reader035.fdocuments.us/reader035/viewer/2022062304/56649ea85503460f94bac1be/html5/thumbnails/32.jpg)
© T Madas
Drawing a Pentagon using a protractor
A pentagon has 5 sidesWe 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?
![Page 33: © 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.](https://reader035.fdocuments.us/reader035/viewer/2022062304/56649ea85503460f94bac1be/html5/thumbnails/33.jpg)
© T Madas
Drawing a Pentagon using a protractor
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•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
![Page 34: © 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.](https://reader035.fdocuments.us/reader035/viewer/2022062304/56649ea85503460f94bac1be/html5/thumbnails/34.jpg)
© T Madas
Drawing a Pentagon using a protractor
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Drawing a Pentagon using a protractor
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© T Madas
Drawing a Pentagon using a protractor
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© T Madas
Drawing a Pentagon using a protractor
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© T Madas
Drawing a Pentagon using a protractor
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© T Madas
Drawing a Pentagon using a protractor
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© T Madas
Drawing a Pentagon using a protractor
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© T Madas
Drawing a Pentagon using a protractor
![Page 42: © 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.](https://reader035.fdocuments.us/reader035/viewer/2022062304/56649ea85503460f94bac1be/html5/thumbnails/42.jpg)
© T Madas
Drawing a Pentagon using a protractor
72°
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8 cm
8 cm
8 c
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8 cm
![Page 43: © 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.](https://reader035.fdocuments.us/reader035/viewer/2022062304/56649ea85503460f94bac1be/html5/thumbnails/43.jpg)
© T Madas
Drawing an Enneagon using a protractor
![Page 44: © 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.](https://reader035.fdocuments.us/reader035/viewer/2022062304/56649ea85503460f94bac1be/html5/thumbnails/44.jpg)
© 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?
![Page 45: © 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.](https://reader035.fdocuments.us/reader035/viewer/2022062304/56649ea85503460f94bac1be/html5/thumbnails/45.jpg)
© T Madas
Drawing an Enneagon using a protractor
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•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
![Page 46: © 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.](https://reader035.fdocuments.us/reader035/viewer/2022062304/56649ea85503460f94bac1be/html5/thumbnails/46.jpg)
© T Madas
Drawing an Enneagon using a protractor
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Drawing an Enneagon using a protractor
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© T Madas
Drawing an Enneagon using a protractor
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© T Madas
Drawing an Enneagon using a protractor
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© T Madas
Drawing an Enneagon using a protractor
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© T Madas
Drawing an Enneagon using a protractor
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© T Madas
Drawing an Enneagon using a protractor
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© T Madas
Drawing an Enneagon using a protractor
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Drawing an Enneagon using a protractor
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© T Madas
Drawing an Enneagon using a protractor
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© T Madas
Drawing an Enneagon using a protractor
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Drawing an Enneagon using a protractor
![Page 58: © 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.](https://reader035.fdocuments.us/reader035/viewer/2022062304/56649ea85503460f94bac1be/html5/thumbnails/58.jpg)
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Drawing an Enneagon using a protractor
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Polygons with Compasses and Straightedge0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
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Constructing Regular
Hexagons
![Page 61: © 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.](https://reader035.fdocuments.us/reader035/viewer/2022062304/56649ea85503460f94bac1be/html5/thumbnails/61.jpg)
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Constructing a Regular Hexagon
Why does it work?
![Page 62: © 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.](https://reader035.fdocuments.us/reader035/viewer/2022062304/56649ea85503460f94bac1be/html5/thumbnails/62.jpg)
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Constructing a Regular Hexagon
Why does it work?
![Page 63: © 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.](https://reader035.fdocuments.us/reader035/viewer/2022062304/56649ea85503460f94bac1be/html5/thumbnails/63.jpg)
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Constructing a Regular Hexagon
Why does it work?
![Page 64: © 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.](https://reader035.fdocuments.us/reader035/viewer/2022062304/56649ea85503460f94bac1be/html5/thumbnails/64.jpg)
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Constructing Regular
Pentagons
![Page 65: © 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.](https://reader035.fdocuments.us/reader035/viewer/2022062304/56649ea85503460f94bac1be/html5/thumbnails/65.jpg)
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•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
![Page 66: © 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.](https://reader035.fdocuments.us/reader035/viewer/2022062304/56649ea85503460f94bac1be/html5/thumbnails/66.jpg)
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Constructing Regular
Octagons
![Page 67: © 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.](https://reader035.fdocuments.us/reader035/viewer/2022062304/56649ea85503460f94bac1be/html5/thumbnails/67.jpg)
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Constructing a Regular Octagon
![Page 68: © 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.](https://reader035.fdocuments.us/reader035/viewer/2022062304/56649ea85503460f94bac1be/html5/thumbnails/68.jpg)
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Constructing Regular
Decagons
![Page 69: © 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.](https://reader035.fdocuments.us/reader035/viewer/2022062304/56649ea85503460f94bac1be/html5/thumbnails/69.jpg)
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•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
![Page 70: © 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.](https://reader035.fdocuments.us/reader035/viewer/2022062304/56649ea85503460f94bac1be/html5/thumbnails/70.jpg)
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