Geometrical Constructions
4.2 Geometrical Constructions – Cheat Sheet
1. Measuring and Drawing Lines and Angles
- Line measurement: Use a ruler (mm precision) for straight edges.
- Angle measurement: Use a protractor, centre hole at vertex, baseline aligned with one side.
- Mark required degree and draw second side with ruler.
2. Constructing a Triangle (Ruler and Compass Only)
Given: Lengths of all three sides (SSS)
Steps:
- Draw the base using ruler.
- With compass, set radius to second side length. Place point at one end of base and draw arc.
- Set compass to third side length. Place point at other end of base and draw arc intersecting first arc.
- Join intersection point to both ends of base.
- Leave arcs visible (required in construction).
Example: Construct triangle ABC where AB = 6 cm, BC = 5 cm, AC = 4 cm.
3. Drawing and Interpreting Nets
- Net: 2D layout of a 3D shape that folds to form the solid.
- Must include correct face sizes and correct relative positions.
- Draw using ruler for straight edges, compass for circles/arcs.
Common Nets:
| Solid | Net Features |
|---|---|
| Cube | 6 equal squares |
| Cuboid | 6 rectangles (pairs of equal sizes) |
| Prism | 2 identical polygon ends + rectangles for sides |
| Pyramid | 1 polygon base + triangles meeting at apex |
| Cylinder | 2 equal circles + 1 rectangle (width = circumference, height = height of cylinder) |
4. Using Nets to Calculate Volume and Surface Area
| Solid | Volume Formula | Surface Area Formula |
|---|---|---|
| Cube | side³ | 6 × side² |
| Cuboid | l × w × h | 2(lw + lh + wh) |
| Prism | area of cross-section × length | Sum of all face areas |
| Pyramid | (1/3) × base area × height | Base area + area of triangular sides |
| Cylinder | πr²h | 2πr² + 2πrh |
5. Example – Construct a Rhombus by Drawing Two Triangles
- Draw one diagonal as base.
- Construct two congruent triangles with compass using given side lengths.
- Join to form rhombus, leaving arcs.