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1. Construct the bisector of an angle.

1. Construct the bisector of an angle. Draw an Acute AOB. Using the vertex O as centre draw an arc to meet the arms of the angle at X and Y. Using X as centre and the same radius draw a new arc. Using Y as centre and the same radius draw an overlapping arc. Mark the point where the arcs meet.

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1. Construct the bisector of an angle.

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  1. 1. Construct the bisector of an angle. • Draw an Acute AOB. • Using the vertex O as centre draw an arc to meet the arms of the angle at X and Y. • Using X as centre and the same radius draw a new arc. • Using Y as centre and the same radius draw an overlapping arc. • Mark the point where the arcs meet. • The bisector is the line from O to this point. A X x x O y B Miss D Brennan 6th year Constructions

  2. 2. Construct the perpendicular bisector of a line segment • Draw the line segment • Using A as centre and a radius greater than half |AB| draw an arc. • Using B as centre and the same radius draw another arc. • Draw a line through the points where the arcs cross. A B Miss D Brennan 6th year Constructions

  3. Line perpendicular to a given line l, passing through a given point not on l. • Draw the line l. • Mark off a point P which is not on l. ( P can be above or below l ) • Using P as centre and the same radius draw two arcs to cut l at R and S. • Using R as centre draw an arc on the opposite side of l to P. • Using S as centre and the same radius draw another arc. • Mark of the point where these arcs meet. Labelled here as T. • Join T to P. P l S R T Miss D Brennan 6th year Constructions

  4. Line perpendicular to a given line l, passing through a given point on l. • Draw the line l. • Mark off a point P which on l. • Using P as centre and the same radius draw two arcs to cut l at A and B. • Double the size of your radius • Using A as centre draw an arc on any side of l. • Using B as centre and the same radius draw another arc on the same side of l. • Mark of the point where these arcs meet. Labelled here as C. • Join C to P and extend. P l A B C Miss D Brennan 6th year Constructions

  5. 5. Line parallel to a given line, through given point. (Set Square Method) • Draw the line l. • Mark off a point P which is not on l. ( P can be above or below l ) • Draw a perpendicular line from P on to l. • Slide the Set Square from the line l up to the point P . • Draw a line from P along the base of the Set Square and extend and label as k. P l k Miss D Brennan 6th year Constructions

  6. 5. Line parallel to a given line, through given point • Draw a line l. • Mark off a point P which is not on l. ( P can be above or below l ) • Draw a line through P to cut the line l at any angle. Label the intersection A • Using A as centre and a radius less than |AP| draw an arc. Add labels C and B • Using P as centre and the same radius draw another arc to cut AP at R. • Use the compass to measure the arc at CB. • Using this as the radius and R as centre draw and arc to cut the outer arc at E. • Draw a line through P and E and label as k. P C k E R l B A Miss D Brennan 6th year Constructions

  7. 6. Divide the line segment [AB] into three equal parts • Draw the line segment [AB]. • Through A draw a line at an acute angle to [AB]. • On this line use circle arcs of the same radius to mark off three segments of equal length [AR], [RS] and [ST]. • Join T to B. • Through S and R draw line segments parallel to [TB] to meet [AB] at D and C. • Now |AC|=|CD|=|DB| A C D B R S T Miss D Brennan 6th year Constructions

  8. 8. Line segment of a given length on a given ray. • Draw a line segment |AB| of required length. (8 cm in this case). • Mark off a point P on ray l. • Using P as centre and a radius equal to |AB| draw an arc to cut l at C. • Join P to C • |PC| will now be 8 cm. 8 cm A B l P 8 cm C Miss D Brennan 6th year Constructions

  9. 9. Angle of a given number of degrees with a given ray as one arm. Example to draw an angle of 45o • Draw the line l • Mark a point A on l. • Place the centre of the protractor on the point A. • Mark a point B on the circumference of the protractor at the angle required 45o in this case. • Remove the protractor and join A to B. • This is the required angle. B 45o A l Miss D Brennan 6th year Constructions

  10. 10. Example: Construct the triangle ABC so that |AB| = 8cm, |AC| = 6cm and |BC| = 7cm. • Draw a line segment 8cm in length. Label the end points and mark the length. • Using a compass with A as centre draw an arc of length 6cm. • With B as centre draw an arc of 7cm. • Mark their point of intersection C. • Join A to C and B to C. C 7 cm 6 cm 8cm A B Miss D Brennan 6th year Constructions

  11. 11. Example: Construct a triangle ABC where |AB| = 12cm, |<BAC| = 65o and |AC| = 9 cm. • Draw a line segment 12cm in length. Name the points and mark the length. • Use a protractor to draw a line at 65o to |AB|. • Use a compass with A as centre and 9cm radius to draw an arc on this line. • Mark the point of intersection C. • Join C to B to complete triangle. C 9cm 65o B A 12cm Miss D Brennan 6th year Constructions

  12. Example: Construct the triangle PQR where |QR|=8cm, |<PQR|=52o and • |<PRQ|=46o • Draw a line segment [QR] 8cm in length. Name the points and mark the length. • At Q using a protractor mark and draw an angle of 52o • At R using a protractor mark and draw an angle of46o • Mark the point of intersection of the two angles. • This is the point P. P 46o 52o Q R 8cm Miss D Brennan 6th year Constructions

  13. 13. Example: Construct a right-angled triangle ABC, given |AB|= 6cm, |<BAC|=90o and |BC|=10cm. • Draw a line segment [AB] 6cm in length. Name the points and mark the length. • At A, using a protractor mark and draw an angle of 90o . • Use a compass with B as centre and 10cm radius to draw an arc on this line. • Mark the point of intersection C. • Join C to B to complete triangle. C 10 cm 6 cm A B Miss D Brennan 6th year Constructions

  14. Example: Construct a right-angled triangle PQR, such that, • |QR| = 7 cm and |<QRP| = 30o • Draw a line segment [QR] 7cm in length. Name the points and mark the length. • At Q using a protractor mark and draw an angle of 90o • At R using a protractor mark and draw an angle of 30o • Extend the lines from Q and R until they meet. This is the vertex P. P 30o 90o Q R 7cm Miss D Brennan 6th year Constructions

  15. 15. Example: Construct a rectangle ABCD, with sides 6 cm and 8 cm. (Protractor) • Draw a line segment [AB] 8 cm in length. Name the points and mark the length. • At A using a protractor mark and draw an angle of 90o • At B using a protractor mark and draw an angle of 90o • Measure lengths of 6 cm along these perpendicular lines.. • Label these points C and D. • Join C to D. D C 6cm 6cm 90o 90o A B 8cm Miss D Brennan 6th year Constructions

  16. 20. Example:Construct a parallelogram ABCD where |AB| = 12cm, |<BAC| = 65o and |AC| = 9 cm. • Draw a line segment 12cm in length. Name the points and mark the length. • Use a protractor to draw a line at 65o to |AB|. • Use a compass with A as centre and 9cm radius to draw an arc on this line. • Mark the point of intersection C. • Draw a line through B parallel to AC and mark off a line segment on this of 9 cm. Call this D. C D • Join C to D to complete parallelogram 9cm 9cm 65o B A 12cm Miss D Brennan 3rd year Constructions

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