1. Constructions

2. Construct a triangle ABC such that angle A = 60⁰, AB = 9cm and AC = 6cm.
Step 1 : Prepare a sketch
Step 2 : draw a long line which will be the base.
Step 3 : open your compasses 9cm and draw two arcs on either side of the base.
Step 4 : measure the line. If it is 9cm, label and continue. If not, rub off and start again.

3. Step 5 : To draw the 60⁰, you can open the compasses any length but it is better if you open it by 6cm ( the length of AC)
Step 6: Draw a long arc from A to cut the base.

4. Step 7: From the point where the long arc hits the base, draw a small arc to cut the long arc.

5. Step 8 : Join A to the point where the two arcs meet.
Step 9: Measure the angle and the line. If they are 60⁰ and 6cm, label and continue.

6. Step 10: Join BC to form triangle ABC

7. Construct triangle PQR such that P = 90⁰, PQ = 8cm and PR = 7cm
Step 1: prepare a sketch
Step 2 : Draw a long line to prepare the base and to a side put a small mark to draw the perpendicular bisector.

8. Step 3: to draw the perpendicular, open the compasses more than half the small line ( even the whole length of it is good).
Step 4 : From one side draw an arc at the top and an arc at the bottom.

9. Step 5: Keeping the compasses open by the same amount, draw two other arcs from the other side of the small line. These two arcs should cross the previous two.

10. Step 6 : Join the two arcs making sure that the length is longer than 7cm ( because that is the length of XZ)
Step 7: Measure the angle. If it is correct, label and continue

11. Step 8 : Next you need to draw the base. Open your compasses 8cm
Step 8 : Next you need to draw the base. Open your compasses 8cm. From point P, mark the 8cm.
Step 9: measure the base. If it is 8cm, label and continue.

12. Step 10 : the height of the triangle is 7cm
Step 10 : the height of the triangle is 7cm. Open your compasses 7cm and from point P, draw a small arc to cut the perpendicular bisector.
Step 11: Measure. If it is 7cm, continue.

13. Step 11. Join points Q to R and label.

14. In triangle ABC, construct i) the locus of points 5cm away from A ii) the locus of points equidistant from B and C
Step 1: Find triangle ABC
Step 2: open compasses by 5cm and put them on point A

15. Step 3: Draw a circle centre A.

16. Step 4: Open the compasses more than half BC and draw the perpendicular bisector.

17. Step 5 : Join the perpendicular bisector.

18. Step 6 : Follow whichever instructions are next given.
Good luck 