Summary — What This Chapter Covers
- Measure and draw lines to the nearest millimetre and angles to the nearest degree.
- Construct a triangle from its three sides using a ruler and compasses only, leaving the arcs visible.
- Build other shapes from triangles, e.g. a rhombus from two triangles.
- Draw, use and interpret nets of cubes, cuboids, prisms and pyramids.
- Use measurements on a net to work out surface area and volume.
1. Measuring and Drawing Lines and Angles
Syllabus 4.2 · Paper 1 & 2
Ruler and protractor
Measure lines in centimetres to the nearest millimetre. To measure an angle, put the centre of the protractor on the vertex and the zero line along one arm, then read from the scale that starts at 0° on that arm. Decide first whether the angle is acute or obtuse, so you do not read the wrong scale.
A protractor only goes to 180°. To draw a reflex angle such as 250°, draw 360° − 250° = 110° and mark the angle on the outside.
Practice Question 1
Explain how to draw an angle of 305° with a 180° protractor.
2. Constructing a Triangle From Three Sides
Syllabus 4.2 · Paper 1 & 2
Ruler and compasses only
- Draw the longest side with a ruler, e.g. AB = 7 cm.
- Open the compasses to the second length (e.g. 5 cm), put the point on A and draw an arc.
- Open the compasses to the third length (e.g. 4 cm), put the point on B and draw an arc that crosses the first one at C.
- Join AC and BC with a ruler. Leave both arcs showing: they are your evidence.
The construction only works if the two shorter sides add up to more than the longest side; otherwise the arcs never meet.
Practice Question 2
Can a triangle be constructed with sides (a) 3 cm, 4 cm, 8 cm, (b) 6 cm, 7 cm, 9 cm? Explain.
What 4024 does not ask
You construct triangles from three sides, and shapes built from triangles. Constructing perpendicular bisectors or angle bisectors is not required in this syllabus.
3. Shapes Built From Triangles
Syllabus 4.2 · Paper 1 & 2
A rhombus from two triangles
Any polygon that can be split into triangles can be constructed one triangle at a time. A rhombus is two isosceles triangles joined along a diagonal.
Worked Example
Describe how to construct a rhombus ABCD with sides 5 cm and diagonal AC = 8 cm. Then calculate the length of the other diagonal BD, so you can check your drawing by measuring.
4. Nets
Syllabus 4.2 · Paper 1 & 2
Flat shapes that fold into solids
A net shows every face of the solid joined edge to edge. When it folds, each edge of the solid is made from two edges of the net that must be the same length.
| Solid | Its net contains |
|---|
| Cube | 6 equal squares (there are 11 different cube nets) |
| Cuboid | 3 pairs of equal rectangles |
| Triangular prism | 2 triangles + 3 rectangles |
| Square-based pyramid | 1 square + 4 triangles |
| Cylinder | 2 circles + 1 rectangle whose length is the circumference |