# Constructions with a ruler and a protractor 0

• Slides: 89

Constructions 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 given angle “Draw an angle of 40 °, with sides of 12 cm and 8 cm” 0 1 2 3 4 126 cm 7 8 5 9 10 11 12 13 14 15 16 17 Start from zero © T Madas

Drawing a given angle 0 80 10 1100 70 12 0 13 60 50 40 14 15 0 20 0 160 10 17 0 0 180 30 80 1 00 70 110 60 50 12 13 0 0 “Draw an angle of 40 °, with sides of 12 cm and 8 cm” 90 0 14 50 0 1 4 30 160 20 0 10 17 0 180 12 cm Line up the dot & line © T Madas

Drawing a given angle 17 18 19 20 21 “Draw an angle of 40 °, with sides of 12 cm and 15 816 cm” 9 7 8 cm 10 11 12 13 14 8 6 5 4 3 2 40° 0 1 12 cm Start from zero © T Madas

Drawing a given angle “Draw an angle of 120 °, with sides of 8 cm and 7 cm” 0 1 2 8 4 cm 5 3 6 7 8 9 10 11 12 13 14 15 Start from zero © T Madas

Drawing a given angle 0 80 10 1100 70 12 0 13 60 14 15 0 0 160 170 180 30 20 10 0 50 40 80 1 00 70 110 6 50 0 12 13 0 0 “Draw an angle of 120 °, with sides of 8 cm and 7 cm” 90 0 14 50 40 1 30 160 20 0 10 17 0 180 8 cm Line up the dot & line © T Madas

15 16 12 13 14 Drawing a given angle 5 6 7 8 9 10 11 “Draw an angle of 120 °, with sides of 8 cm and 7 cm” 4 7 c 3 m 0 1 2 120° 8 cm Start from zero © T Madas

Drawing a given reflex angle “Draw an angle of 320 °, with sides of 8 cm and 6 cm” in order to draw a reflex angle we can draw the angle missing to complete a full turn i. e. 360° So we draw a … … 40 ° angle … … then mark … … the outside of this angle 320° 40° © T Madas

Drawing a given reflex angle “Draw an angle of 320 °, with sides of 8 cm and 6 cm” 0 1 2 8 4 cm 5 3 6 7 8 9 10 11 12 13 14 15 Start from zero © T Madas

Drawing a given angle 0 80 10 1100 70 12 0 13 60 14 15 0 0 160 170 180 30 20 10 0 50 40 80 1 00 70 110 6 50 0 12 13 0 0 “Draw an angle of 320 °, with sides of 8 cm and 6 cm” 90 0 14 50 40 1 30 160 20 0 10 17 0 180 8 cm Line up the dot & line © T Madas

Drawing a given angle 15 16 17 18 19 14 “Draw an angle of 320 °, with sides of 8 cm and 6 cm” 13 9 7 10 11 12 8 6 5 62 4 3 cm 1 0 320° 40° 8 cm Start from zero © T Madas 2

Drawing a given reflex angle “Draw an angle of 230 °, with sides of 7 cm and 5 cm” in order to draw a reflex angle we can draw a straight line first i. e. 180° Then draw a… … 50° angle … … then mark … … both angles 230° 180° 50° © T Madas

Drawing a given reflex angle “Draw an angle of 230 °, with sides of 7 cm and 5 cm” 0 1 2 7 4 cm 5 3 6 7 8 9 10 11 12 13 14 Start from zero © T Madas

Drawing a given reflex angle “Draw an angle of 230 °, with sides of 7 cm and 5 cm” 0 1 2 3 4 5 6 7 8 9 10 11 12 13 7 15 cm 16 14 17 18 19 20 21 22 23 © T Madas

Drawing a given reflex angle “Draw an angle of 230 °, with sides of 7 cm and 5 cm” Line up the dot & line 40 30 14 15 0 20 0 16 10 17 0 0 0 180 0 14 50 40 1 30 160 20 0 10 17 0 180 80 70 100 110 6 5 0 0 12 13 0 0 0 80 10 0 11 0 70 12 0 60 13 50 7 cm 90 © T Madas

Drawing a given reflex angle “Draw an angle of 230 °, with sides of 7 cm and 5 cm” Start from zero 230° 0 7 cm 2 cm 1 50° 5 3 4 5 6 7 8 © T Madas

Drawing a Triangle (SAS) Draw a triangle with sides of 7 cm and 5. 5 cm and the contained angle of 50° 0 1 2 73 cm 4 5 6 7 8 9 10 11 12 13 14 15 16 Start from zero © T Madas 1

Drawing a Triangle (SAS) 0 80 10 1100 70 12 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 Draw a triangle with sides of 7 cm and 5. 5 cm and the contained angle of 50° 90 0 14 50 40 1 30 160 20 0 10 17 0 180 7 cm Line up the dot & line © T Madas

19 18 15 16 17 Drawing a Triangle (SAS) 3 50° 0 1 2 5. 5 4 5 cm 6 7 8 9 10 11 12 13 14 Draw a triangle with sides of 7 cm and 5. 5 cm and the contained angle of 50° 7 cm Start from zero © T Madas

Drawing a Triangle (SAS) 0 1 Draw a triangle with sides of 7 cm and 5. 5 cm and the contained angle of 50° 2 3 4 5 6 7 8 10 12 5. 5 11 cm 9 14 15 7 cm 13 50° 16 17 18 19 20 © T Madas

Drawing a Triangle (ASA) Draw a triangle with a side of 10 cm and adjacent angles of 40° and 70° 0 1 2 3 10 4 5 cm 6 7 8 9 10 11 12 13 14 15 16 Start from zero © T Madas 1

Drawing a Triangle (ASA) 0 80 10 1100 70 12 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 Draw a triangle with a side of 10 cm and adjacent angles of 40° and 70° 90 0 14 50 0 1 4 30 160 20 0 10 17 0 180 10 cm Line up the dot & line © T Madas

Drawing a Triangle (ASA) 0 80 10 1100 70 12 0 13 60 80 1 00 70 110 6 50 0 12 13 0 0 Draw a triangle with a side of 10 cm and adjacent angles of 40° and 70° 90 50 40 30 14 15 0 20 0 160 10 17 0 0 180 10 cm 0 14 50 0 1 4 30 160 20 0 10 17 0 180 Line up the line & dot © T Madas

Drawing a Triangle (ASA) 18 19 20 Draw a triangle with a side of 10 cm and adjacent 16 15 angles of 40° and 70° 14 17 9 7 10 11 12 13 8 6 5 4 3 2 0 1 10 cm © T Madas 2

3 4 Drawing a Triangle (ASA) 5 6 7 Draw a triangle with a side of 10 cm and adjacent angles of 40° and 70° 8 9 10 11 12 13 14 15 16 17 18 10 cm 19 20 21 2 22 © T Madas

Drawing a Triangle (ASA) Draw a triangle with a side of 10 cm and adjacent angles of 40° and 70° 40° 10 cm © T Madas

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 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

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 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 8 9 10 11 12 © T Madas 1

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 Hexagon using a protractor © T Madas

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 8 9 10 © T Madas 1

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

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 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 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

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 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 8 9 10 11 12 © T Madas 1

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 using a protractor © T Madas

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 5 6 7 8 9 10 11 12

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 8 © T Madas 9

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

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 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 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 0 160 170 180 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 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 8 9 10 11 12 © T Madas 1

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 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 © T Madas 8 9 10 11 12 13 14 15

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

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 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 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

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 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 8 9 10 11 12 © T Madas 1

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 using a protractor © T Madas

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 5 6 7 8 9 10 11 12 13 1

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 8 9 10 1 © T Madas

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 8 9 10 11 12 © T Madas