Geometrical Constructions (Copy)
Measurement, Constructions, and Nets Cheat Sheet (IGCSE Mathematics 0580 – CORE)
Topic: Drawing Lines, Angles, Triangles, and Nets
1. Measuring and Drawing Lines and Angles
- Use a ruler to measure and draw straight lines accurately.
- Use a protractor to measure and draw angles.
- Always label lines and angles clearly.
2. Constructing a Triangle (Given 3 Sides)
Steps to construct a triangle with only a ruler and compass:
- Draw the base line accurately with a ruler.
- Place the compass at one end of the base, open it to the length of the second side, and draw an arc.
- Without changing the compass width, place it at the other end of the base and draw another arc.
- The point where the arcs meet is the third vertex of the triangle.
- Join the vertex to both ends of the base using a ruler.
- Always show construction arcs — they must be visible.
Important:
- Ruler for all straight lines.
- Compass only for arcs.
- No need to measure angles unless asked.
3. Drawing, Using, and Interpreting Nets
- Net: A 2D layout that can be folded to form a 3D solid.
- Nets must show all faces correctly shaped and joined.
- Nets help calculate surface areas and understand the structure of solids.
Common Nets:
| Solid | Net Features |
|---|---|
| Cube | 6 equal squares |
| Cuboid | 6 rectangles (opposite faces equal) |
| Prism | Two identical polygonal faces and rectangles joining them |
| Pyramid | Base polygon and triangles meeting at a point (apex) |
4. Example: Draw a Net for a Cube
- Draw 6 equal squares connected edge-to-edge.
- Common layout: 4 squares in a row (side faces), 1 on top, 1 on bottom.
5. Using Nets to Calculate Surface Area and Volume
- Surface Area: Add areas of all faces.
- Volume of Cube: side³
- Volume of Cuboid: length × width × height
- Volume of Prism: area of cross-section × length
- Volume of Pyramid: (1/3) × area of base × height
Use measurements from the net if dimensions are given.
Important Construction Tips
- Always use a sharp pencil for accurate drawings.
- Label all important points, sides, and angles.
- Construction arcs must not be erased.
- Use a ruler for every straight edge — no freehand lines allowed.
This covers all CORE-level skills for measuring, constructing basic figures, and drawing/using nets without involving advanced constructions like bisectors.