PowerPoint Presentation

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.

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1Miss D Brennan 6th year Math's2. Construct the perpendicular bisector of a line segmentDraw 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.

ABMiss D Brennan 6th year Constructions2Miss D Brennan 6th year Math'sLine 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.

RSPTlMiss D Brennan 6th year Constructions3Miss D Brennan 6th year Math'sLine 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 radiusUsing 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.

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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.

PlkMiss D Brennan 6th year Constructions5Miss D Brennan 6th year Math's5. Line parallel to a given line, through given pointDraw 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 BUsing 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.

klEBCAPRMiss D Brennan 6th year Constructions6Miss D Brennan 6th year Math's6. Divide the line segment [AB] into three equal partsDraw 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|

DCTSABRMiss D Brennan 6th year Constructions7Miss D Brennan 6th year Math's8. 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.

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9. Angle of a given number of degrees with a given ray as one arm. Example to draw an angle of 45oDraw the line lMark 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.

BAl45oMiss D Brennan 6th year Constructions9Miss D Brennan 6th year Math's10. 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.8cmAB7 cm6 cmCMiss D Brennan 6th year Constructions10Miss D Brennan 6th year Math's

11. Example: Construct a triangle ABC where |AB| = 12cm, |