1. Using a protractor, draw the angles:
Starter
Using a protractor, draw the angles:
26°
154°
201°

2. Construct a triangle PQR with lines PQ = 8cm, QR = 5cm and PQR = 40°.
40° P Q
8cm
Draw an 8cm line and label the ends P and Q. This is the line PQ.
Place the centre of the protractor on Q with the 0° line pointing to P.
Measure a 40° angle clockwise from 0°. Mark it with a dot.
Draw a 5cm line from Q through the dot. Label the end of this line R.
Join up P and R to complete the triangle.

3. Construct a triangle PQR with lines PQ = 8cm, PQR = 40° and RPQ = 30°. .
30°
40° P
8cm Q
Draw an 8cm line and label the ends P and Q. This is the line PQ.
Place the centre of the protractor on Q with the 0° line pointing to P.
Measure a 40° angle clockwise from 0°. Mark it with a dot.
Draw a line from Q through the dot.
Place the centre of the protractor on P with the 0° line pointing to Q.
Measure a 30° angle anticlockwise from 0°. Complete as with other angle.
Point R is where the two lines meet.

4. Construct a triangle ABC with side lengths AB = 9cm, AC = 5cm and BC = 7cm.
Draw a 9cm line and label the ends A and B. This is the line AB.
Set your compasses to 5cm and with the point on A draw an arc.
Set your compasses to 7cm and with the point on B draw an arc.
Label this point C and join A to C then B to C to get the lines AC and BC.

5. Plenary
Accurately construct the quadrilateral using the given information
5cm
100°
120°
2cm
6cm
How long is the top side of the quadrilateral?

6. Starter A Draw a circle and mark a point A on its circumference. A B
Keep the compasses set at the size of the radius, and from point A draw an arc that cuts the circle at point B. A B
Repeat the process until six point are marked on the circumference. Join the points to make a regular hexagon.

7. Loci “Loci” is the plural of “Locus”.
A Locus is the path you would follow if you were given certain instructions.
Eg. You must walk so that you are always 5 metres inside the fence surrounding the school fields. Where must you walk?
Eg. A goat is tethered to a rope that is 4 metres long. Show the region the goat can reach.

8. Loci There are only FOUR loci.
(1) A fixed distance from a fixed point.
(2) A fixed distance from a fixed line.
(3) The same distance from two fixed points.
(4) The same distance from two fixed lines.
Lets look at the four loci individually

9. A fixed distance from a fixed point
We end up with a circle of radius r

10. A fixed distance from a fixed line
We end up with parallel lines.
But what about at the ends?

11. The same distance from two fixed points
Step 1 Open a pair of compasses to a distance that is slightly greater than half the distance between the points.
Step 2 From one point draw two arcs, one above the points and one below.
Step 3 Repeat this from the other point.
Step 4 Join where the arcs cross together.

12. The same distance from two fixed lines
Step 1 On each line draw an arc, centred at the point where the lines cross.
Step 2 From each of these points draw two more arcs.
Step 3 Join where the arcs cross to where the lines cross.

13. Layton
Moorby
Newdon
The map above, drawn to a scale of 4cm to 1 km, shows the positions of three villages, Layton, Moorby and Newdon.
Simon’s house is the same distance from Moorby as it is from Layton. The house is also less than ¾ km from Newdon.
Mark on the map the possible positions of Simon’s house. Show your construction lines clearly.