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Construction 1a Construction 1a Construct a triangle (ASA)Construct a triangle (ASA)

Construction 1b Construction 1b Construct a triangle (SAS)Construct a triangle (SAS)

Construction 2 Construction 2 Construct the bisector of an angleConstruct the bisector of an angle

Construction 3 Construction 3 Construct the perpendicular bisector of a line segment.Construct the perpendicular bisector of a line segment.

Construction 4 Construction 4 Construct the circumcircle of a triangle.Construct the circumcircle of a triangle.

Construction 5 Construction 5 Construct the incircle of a triangle. Construct the incircle of a triangle.

Construction 6 Construction 6 Divide the line segment [ab] into three equal parts. Divide the line segment [ab] into three equal parts.

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Construct the triangle pqr where |qr|=8cm, |<pqr|=52o and |<prq|=46o (A S A)

• Draw a line segment [qr] 8cm in length. Name the points and mark the length.

|qr|=8cm

46°52°

p

rq

• At q using a protractor mark and draw an angle of 52o.

• At r mark and draw an angle of 46o

• Mark the point of intersection of the two angles.

• This is the point p.

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END OF CONSTRUCTION

Construct a triangle abc where |ab| = 12cm, |<bac|=65o and |ac| = 9 cm (S A S)

65°

ba

c

|ab|=12cm

|ac|=9cm

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• 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 and complete labels.

Construct the bisector of an angle• Draw the angle 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.

y

x

o

a

b

xxxx

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Construct the perpendicular bisector of a line segment

• Draw the line segment

a b

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END OF CONSTRUCTION

• 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.

Construct the circumcircle of a triangle

• Draw the triangle abc

O

a

b

c

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• Construct the perpendicular bisector of [ab]• Construct the perpendicular bisector of [ac]• The bisectors meet at o the circumcentre of the triangle• Using o as centre and |oa| as radius construct the circumcircle of the triangle abc

Construct the incircle of a triangle

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• Draw the triangle abc• Construct the bisector of angle abc as shown.• Construct the bisector of angle acb as shown.• The bisectors meet at point o, the incentre of the triangle• Using o as centre construct the incircle of the triangle abc

oox

x

o

a

b c

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|

dc

t

s

a b

r

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END OF CONSTRUCTION