1. 04/12/2018
Drawing in maths – KEY WORDS
Sketch
Does not need to be accurate. Just needs to show the key features (rough shape, dimensions or measurements labelled). No need to use ruler or other equipment.
Plot
Usually on a graph or chart, using given coordinates or data. Must be accurate according to the scale given.
Construct
Must be absolutely accurate. All lengths and angles must be measured out perfectly to within 2mm or 2 degrees. Must use correct equipment to get that accuracy.

2. CONSTRUCTING TRIANGLES
04/12/2018
CONSTRUCTING TRIANGLES

3. A ruler marked in cm and mm
04/12/2018
Before you begin make sure you have the following equipment:
A ruler marked in cm and mm
A protractor
A pair of compasses
A sharp pencil

4. To construct a triangle, given 1 side and 2 angles.
04/12/2018
Example
To construct a triangle, given 1 side and 2 angles.
Construct a triangle of side, 9 cm with angles of 35o and 65o.
1. Draw a straight line 9 cm long.
2. Use a protractor to draw angles of 35o and 65o on either end of line.
3. Draw straight lines from A and B to point of intersection to form the triangle. A B
9 cm

5. Don’t forget...leave your construction lines visible
04/12/2018
Use this method to construct the following triangles...
Side 6cm, angles 45° and 30°
Side 5cm, angles 80° and 25°
Side 8cm, angles 15° and 70°
Side 10cm, angles 105° and 50°
Side 4cm, angles 25° and 125°
Don’t forget...leave your construction lines visible

6. To construct a triangle, given 2 sides and 1 angle.
04/12/2018
Example
To construct a triangle, given 2 sides and 1 angle.
Construct a triangle of sides, 10 cm and 7cm with an angle of 115o.
1. Draw a straight line 10 cm long.
2. Use a protractor to draw an angle of 115o on either end of line.
7 cm
3. Mark off a length of 7 cm.
4. Join end points to form the required triangle.
115o A B
10 cm

7. Don’t forget...leave your construction lines visible
04/12/2018
Use this method to construct the following triangles...
Sides 4cm, 7cm and angle 65°
Sides 5cm, 8cm and angle 50°
Sides 8cm, 3cm and angle 85°
Sides 10cm, 9cm and angle 100°
Sides 6cm, 5cm and angle 130°
Don’t forget...leave your construction lines visible

8. To construct a triangle, given 3 sides.
04/12/2018
Example
To construct a triangle, given 3 sides.
Construct a triangle of sides 7 cm, 3½ cm and 10 cm.
1. Using the longest side as the base, draw a straight line 10 cm long.
2. Set compass to 7 cm, place at A and draw an arc.
3. Set compass to 3½ cm, place at B and draw an arc to intersect the first one.
4. Draw straight lines from A and B to point of intersection.
7 cm
3½ cm A B
10 cm

9. Don’t forget...leave your construction lines visible
04/12/2018
Use this method to construct the following triangles...
Sides 4cm, 7cm and 8cm
Sides 5cm, 8cm and 10cm
Sides 8.5cm, 3cm and 6.5cm
Sides 8.4cm, 9.6cm and 7.1cm
Equilateral with sides 6cm
Isosceles with sides 6.5, 6.5 and 4
Don’t forget...leave your construction lines visible

10. Triangle construction revision
04/12/2018
Triangle construction revision
Constructing from 1 side, 2 angles (ASA)
1) 45°, 50°, 7cm
2) 30°, 70°, 3cm
3) 70°, 110°, 6.5cm
4) 53°, 20°, 6cm
5) 120°, 42°, 12.5cm
6) 135°, 12°, 9cm
Constructing from 2 sides, 1 angle (SAS)
1) 45°, 4cm, 7cm
2) 30°, 6cm, 3cm
3) 70°, 4.5cm, 6.5cm
4) 53°, 8cm, 11cm
5) 120°, 4cm, 12.5cm
6) 135°, 9cm, 9cm
Constructing from 3 sides (SSS)
1) 8cm, 10cm, 6cm ) 7cm, 4cm, 9cm
3) 11cm, 6cm, 8cm ) 2.5cm, 3cm, 4.5cm
5) 6.2cm, 4.5cm, 7.3cm 6) 9cm, 10cm, 3.6cm

11. 04/12/2018 A B
8 cm
7 cm
6 cm
Explain why a triangle with sides 2 cm,10 cm and 7 cm cannot be constructed. A B
9 cm
7 cm
4 cm
Under what conditions can it be guaranteed that a triangle can be constructed from 3 given lengths? A B
10 cm
7 cm
3½ cm
The sum of the lengths of the smaller sides must exceed the length of the longest side.

12. CONSTRUCTING BISECTORS
04/12/2018
CONSTRUCTING BISECTORS

13. 04/12/2018
Sometimes you will have to construct the perpendicular bisector to a line
Perpendicular means...
Bisector means...

14. Don’t forget...leave your construction lines visible
04/12/2018
Step by step...
1: Draw a line
2: Open your compasses to about of the way along your line
3: Draw arcs above and below, with your compass point at one end of the line
4: Repeat at the other end of the line WITHOUT changing the compass setting
5: Join where the arcs cross using a pencil and ruler...this is the perpendicular bisector
Don’t forget...leave your construction lines visible

15. 04/12/2018 Constructing a perpendicular bisector x
1) Place your compasses at one end of the line and draw an arc just over half way.
2) Now place the compasses at the other end of the line WITHOUT adjusting the length. Draw another arc.
3) Finally, use your ruler to draw a straight line through the two intersects of the arcs. x

16. Don’t forget...leave your construction lines visible
04/12/2018
Task
Now use this method to construct the perpendicular bisector of the following line lengths....
Length 6.5 cm
Length 9.8 cm
Length 10.7 cm
Length 43 mm
Length 27 mm
Don’t forget...leave your construction lines visible

17. 04/12/2018 Constructing an angle bisector x
1) Place your compasses at the base of the angle and draw an arc about half way, intersecting both lines
2) Now place the compasses at a point where the arc intersects the line and draw another arc above the original arc
3) Do exactly the same as step 3 on the other intersect WITHOUT adjusting the length of the compasses.
4) Finally draw a line through the intersect of the mini arc and the base of the angle. x

18. Don’t forget...leave your construction lines visible
04/12/2018
Task
Draw and bisect the following angles....
83°
104°
73°
19°
99°
65°
Don’t forget...leave your construction lines visible

19. OTHER WAYS TO USE CONSTRUCTION
04/12/2018
OTHER WAYS TO USE CONSTRUCTION

20. To construct a Regular Hexagon.
04/12/2018
To construct a Regular Hexagon.
1. Draw a circle of any radius.
2. With compass fixed at 1 radius place anywhere on the circumference and mark off 6 arcs.
3. Join intersections of arcs together to form a regular hexagon.

21. 04/12/2018
LOCI BASICS

22. Shade the points less than 4cm from P
04/12/2018
Shade the points less than 4cm from P
A circle p
4 cm

23. 04/12/2018
Draw a line showing the points an equal distance from A and B p1 p2
The perpendicular bisector of the line joining the points.
3. Place compass at B, with same distance set and draw 2 arcs to intersect first two.
2. Place compass at A, set over halfway and draw 2 arcs
4. Draw the perpendicular bisector through the points of intersection.
1. Join both points with a straight line. A B

24. 04/12/2018 Draw the locus of points 4cm from AB
Place compass on ends of line and draw semi-circles of radii 4cm.
Draw 2 lines parallel to AB of equal length and 4cm from it.
4cm

25. 04/12/2018
Shade the region that is more than 2cm away from AB B A C D

26. Shade the points closer to AB than AC
04/12/2018
Shade the points closer to AB than AC A B C
1. Place compass at A and draw an arc crossing both arms.
3. Draw straight line from A through point of intersection for angle bisector.
2. Place compass on each intersection and set at a fixed distance. Then draw 2 arcs that intersect.
The angle bisector A B C

27. TWO POINTS → perpendicular bisector ONE LINE → running track or line
04/12/2018
The four loci you need to know
Decide for each statement in the question what it is referring to out of these four options, and draw the appropriate locus…
ONE POINT → circle
TWO POINTS → perpendicular bisector
ONE LINE → running track or line
TWO LINES → angle bisector

28. 04/12/2018
COMBINING LOCI

29. 04/12/2018
Suppose two goats, Archimedes and Babbage, occupy a fenced rectangular area of grass of length 18 m and width 12 m.
Archimedes is tethered so that he can only eat grass that is within 12 m from the fence PQ and Babbage is tethered so that he can only eat grass that is within 14 m of post R.
Describe how we could find the area that both goats can graze.

30. 04/12/2018
Combining loci
Look for the words “shade the region” to know it is a loci question
For each of the statements given, decide if it is referring to 1 point, 2 points, 1 line or 2 lines, and so which construction you need to be doing
If there is a scale given, use that carefully to decide how big to make any circle or running track
Once all loci are complete, re-read the statements and use them to decide which region needs to be shaded

31. INSIDE the blue circle…
04/12/2018
BELOW the pink line…
INSIDE the blue circle…
2 points – perpendicular bisector
1 point – circle

32. 04/12/2018
12cm
8cm

33. 04/12/2018
5cm
3.5cm

34. 04/12/2018
12cm
4cm
4cm
10cm

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