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.
yXOABxxMiss D Brennan 6th year Constructions
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.
lPABCMiss D Brennan 6th year Constructions4Miss D Brennan 6th
year Math's
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.
8 cm8 cmABPClMiss D Brennan 6th year Constructions8Miss D
Brennan 6th year Math's
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, |