Constructions with a ruler and a protractor

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Presentation transcript:

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 acute angle Drawing a given angle drawing a given acute angle © T Madas

Drawing a given angle “Draw an angle of 40 °, with sides of 12 cm and 8 cm” 12 cm 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 from zero © T Madas

Drawing a given angle “Draw an angle of 40 °, with sides of 12 cm and 8 cm” 180 10 20 170 160 30 150 40 140 50 130 60 120 70 110 80 100 90 12 cm Line up the dot & line © T Madas

Drawing a given angle “Draw an angle of 40 °, with sides of 12 cm and 8 cm” 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 8 cm 40° 12 cm Start from zero © T Madas

drawing a given obtuse angle Drawing a given angle drawing a given obtuse angle © T Madas

Drawing a given angle “Draw an angle of 120 °, with sides of 8 cm and 7 cm” 8 cm 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 from zero © T Madas

Drawing a given angle “Draw an angle of 120 °, with sides of 8 cm and 7 cm” 180 10 20 170 160 30 150 40 140 50 130 60 120 70 110 80 100 90 8 cm Line up the dot & line © T Madas

Drawing a given angle 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 “Draw an angle of 120 °, with sides of 8 cm and 7 cm” 7 cm 120° 8 cm Start from zero © T Madas

Drawing a given reflex angle drawing a given reflex angle method 1 drawing a given reflex angle © 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” 8 cm 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 from zero © T Madas

Drawing a given angle “Draw an angle of 320 °, with sides of 8 cm and 6 cm” 180 10 20 170 160 30 150 40 140 50 130 60 120 70 110 80 100 90 8 cm Line up the dot & line © T Madas

Drawing a given angle “Draw an angle of 320 °, with sides of 8 cm and 6 cm” 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 6 cm 40° 8 cm 320° Start from zero © T Madas

Drawing a given reflex angle drawing a given reflex angle method 2 drawing a given reflex angle © T Madas

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” 7 cm 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 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 14 15 16 17 18 19 20 21 22 23 7 cm © 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 180 10 20 170 160 30 150 40 140 50 130 60 120 70 110 80 100 90 7 cm © T Madas

Drawing a given reflex angle “Draw an angle of 230 °, with sides of 7 cm and 5 cm” Start from zero 230° 7 cm 50° 5 cm © 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 Triangle (SAS) drawing a triangle given: 2 of its sides and the contained angle of these sides © 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 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 7 cm Start from zero © T Madas

Drawing a Triangle (SAS) Draw a triangle with sides of 7 cm and 5.5 cm and the contained angle of 50° 180 10 20 170 160 30 150 40 140 50 130 60 120 70 110 80 100 90 7 cm Line up the dot & line © 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 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 5.5 cm 50° 7 cm Start from zero © T Madas

Drawing a Triangle (SAS) Draw a triangle with sides of 7 cm and 5.5 cm and the contained angle of 50° 5.5 cm 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° 7 cm © T Madas

Drawing a Triangle (ASA) drawing a triangle given: 1 of its sides and the 2 adjacent angles to that side © 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 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 10 cm Start from zero © T Madas

Drawing a Triangle (ASA) Draw a triangle with a side of 10 cm and adjacent angles of 40° and 70° 180 10 20 170 160 30 150 40 140 50 130 60 120 70 110 80 100 90 10 cm Line up the dot & line © T Madas

Drawing a Triangle (ASA) Draw a triangle with a side of 10 cm and adjacent angles of 40° and 70° 180 10 20 170 160 30 150 40 140 50 130 60 120 70 110 80 100 90 10 cm Line up the line & dot © 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 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 10 cm © 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 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 10 cm © T Madas

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

Drawing a Hexagon using a protractor Regular Hexagon © 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 13 14 15 16 17 18 19 20 21 22 23 © T Madas

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

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

Drawing a Hexagon using a protractor © 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 © 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 © T Madas

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

Drawing an Octagon using a protractor Regular Octagon © 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 13 14 15 16 17 18 19 20 21 22 23 © T Madas

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

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

Drawing an Octagon using a protractor © 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 © 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 © T Madas

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

Drawing a Pentagon using a protractor Regular Pentagon © 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 13 14 15 16 17 18 19 20 21 22 23 © T Madas

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

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

Drawing a Pentagon using a protractor © 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 Pentagon using a protractor © T Madas

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

Drawing an Enneagon using a protractor Regular Enneagon © 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 13 14 15 16 17 18 19 20 21 22 23 © T Madas

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

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

Drawing an Enneagon using a protractor © 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 Enneagon using a protractor © 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 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 © T Madas

Drawing an Enneagon using a protractor © T Madas

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

© T Madas