1. Triangle Given Sides and Angle
Bisect Angle
Bisect Line
Incircle
Circumcircle
Centroid
Triangle Given Sides and Angle
Triangle Given Three Sides

2. Bisect the given angle BAC without using a protractor.
Show all construction lines. B A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 C 2

3. Construct the perpendicular bisector of line segment [AB].
Show all construction lines. 1 2 3 4 5
1 0
2 0
3 0
4 0
5 0 6 7 8 9 10 11
6 0
7 0
8 0
9 0
10 0
11 0 A B 3

4. Construct a triangle ABC with | AB | = 6 cm, |  BAC | = 50º
and |  ABC | = 70º. Label your diagram clearly. C 10 20 30 40 50 60 70 80 90
100
110
120
130
140
150
160
170
180 10 20 30 40 50 60 70 80 90
100
110
120
130
140
150
160
170
180 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10
50º
70º 1 2 3 4 5 6 7 8 9 10 A
6 cm B 4

5. Angles in an equilateral triangle are all 60º2 3 4 5 6 7 8 9 10 1
LCO 2008 Paper 2 Question 4 (c) (i)
Construct an equilateral triangle PQR of side 8 cm. 2 3 4 5 6 7 8 9 10 1 R
Angles in an equilateral triangle are all 60º 10 20 30 40 50 60 70 80 90
100
110
120
130
140
150
160
170
180
60º 2 3 4 5 6 7 8 9 10 1 P Q 5

6. LCO 2006 Paper 2 Question 4 (c) (i)
(i) Construct a triangle ABC in which | AB | = 6·5 cm, | BC | = 2·5 cm
and | AC | = 6 cm.
Set your compass so that the pencil and point are 2·5 cm apart
Similarly draw an arc with your compass set at 6 cm and with A as the centre 10 C
6 cm
2·5 cm A B 1 2 3 4 5
1 0
2 0
3 0
4 0
5 0 6 7 8 9 10 11
6 0
7 0
8 0
9 0
10 0
11 0
6·5 cm
Draw the base line AB 6·5 cm in length
With B as centre draw an arc with the point of the compass
Mark the intersection of the arcs as C and draw the lines AC and BC

7. Construct a triangle PQR with | PQ | = 8 cm, | QR | = 10 cm
and |  PQR| = 30º. Label your diagram clearly. R
10 cm 10 20 30 40 50 60 70 80 90
100
110
120
130
140
150
160
170
180 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10
30º P 1 2 3 4 5 6 7 8 9 10 Q
8 cm 7

8. JCH 2010 Paper 2 Question 3 (b) (i)
Show how to construct the triangle XYZ, with sides
| XY | = 10 cm, | XZ | = 8 cm and | YZ | = 5 cm.
Similarly draw an arc with your compass set at 5 cm and with Y as the centre
Mark the intersection of the arcs as Z and draw the lines XZ and YZ
Draw the base line [XY] 10 cm in length
Set your compass so that the pencil and point are 8 cm apart Z
With X as centre draw an arc
8 cm
5 cm X Y 1 2 3 4 5
1 0
2 0
3 0
4 0
5 0 6 7 8 9 10 11
6 0
7 0
8 0
9 0
10 0
11 0
10 cm 8

9. JCH 2008 Paper 2 Question 3 (b) (i)
Construct a triangle of sides 11 cm, 8 cm and 6 cm.
With the end point as centre draw an arc
Set your compass so that the pencil and point are 6 cm apart
Mark the intersection of the arcs and draw the lines
Similarly draw an arc with your compass set at 8 cm and with the start point as the centre
Draw the base line 11 cm in length
8 cm
6 cm 1 2 3 4 5
1 0
2 0
3 0
4 0
5 0 6 7 8 9 10 11
6 0
7 0
8 0
9 0
10 0
11 0
11 cm 9

10. JCH 2006 Paper 2 Question 3 (c) (i)
Construct a triangle of sides 8 cm, 7 cm and 6 cm.
All construction lines must be clearly shown in each case.
With the end point as centre draw an arc
Set your compass so that the pencil and point are 6 cm apart
Similarly draw an arc with your compass set at 7 cm and with the start point as the centre
Mark the intersection of the arcs and draw the lines
Draw the base line 8 cm in length
7 cm
6 cm 1 2 3 4 5
1 0
2 0
3 0
4 0
5 0 6 7 8 9 10 11
6 0
7 0
8 0
9 0
10 0
11 0
8 cm 10

11. JCH 2003 Paper 2 Question 3 (b) (i)
Construct a triangle XYZ in which | XY | = 10 cm, | YZ | = 7 cm
and | XZ | = 5 cm.
Similarly draw an arc with your compass set at 7 cm and with Y as the centre
Draw the base line [XY] 10 cm in length
Set your compass so that the pencil and point are 5 cm apart
With X as centre draw an arc
Mark the intersection of the arcs as Z and draw the lines XZ and YZ Z
5 cm
7 cm X Y 1 2 3 4 5
1 0
2 0
3 0
4 0
5 0 6 7 8 9 10 11
6 0
7 0
8 0
9 0
10 0
11 0
10 cm 11

12. JCH 2006 Paper 2 Question 3 (c) (ii)
Construct the incircle of the triangle.
All construction lines must be clearly shown in each case.
Construct the bisector of two of the angles using circle arcs
The intersection of the bisectors is the centre of the incircle 12

13. LCO 2012 Project Maths Paper 2 Question 6A (a)
(b) Construct the circumcentre and circumcircle of the triangle
below. Show all construction marks clearly.
Using O as centre and |OC| as radius construct the circumcircle.
Construct the perpendicular bisector of [AC] using circle arcs.
Construct the perpendicular bisector of [AB] using circle arcs.
The bisectors meet at O the circumcentre of the triangle. A 15 O B C

14. LCO 2011 Project Maths Paper 2 Question 6A (a)
(a) Show clearly how to construct the centroid of the triangle
below. (Note: all instruments are permitted. If you are using
measurements, show your measurements and calculations.)
Construct the perpendicular bisector of [AB] using circle arcs.
Construct the perpendicular bisector of [AC] using circle arcs.
Join the perpendicular of [AC] to vertex B.
Join the perpendicular of [AB] to vertex C.
The medians meet at O ,the centroid of the triangle. 15 A B O C 14