# Constructions

Accurate drawings made with a pair of compasses and a ruler, without measuring angles.

Maths (school) · Part 07: Shape and space · Card 9 of 9 · Last updated 2026-10-19

## Analogy

Like drawing with strings: the compass sets exact distances.

## Example

**Perpendicular bisector**

Set compasses over half the line
Draw arcs from both ends
Join where the arcs cross
This line cuts the original at 90 degrees

## In practice

Architects and engineers use constructions to draw precise plans.

## Practice

### Flashcards

- **What do the arcs show in a perpendicular bisector construction?** Points equally far from both ends of the line.

## Questions people ask

### Why must you keep the compass width the same?

The arcs must be equal distances from each end, and this equal distance is what makes the new line a perfect bisector. Changing the width halfway breaks the symmetry and the result will not be accurate. The arcs from each end must use the same radius, or the crossing points will be wrong.

### Why should you leave your construction lines in?

Construction arcs show the examiner your method. Rubbing them out can lose marks, as the drawing might look like it was done by measuring with a protractor. Keep your lines faint but visible. They prove you used compasses, and they are usually part of what the mark scheme asks to see.

## Related concepts

- [Congruent shapes](https://studyvisually.com/learn/science/maths-school/maths-school-part-7/maths-school-part-7-concept-5)
- [Similar shapes](https://studyvisually.com/learn/science/maths-school/maths-school-part-7/maths-school-part-7-concept-6)
- [Bearings](https://studyvisually.com/learn/science/maths-school/maths-school-part-7/maths-school-part-7-concept-7)
- [Vectors](https://studyvisually.com/learn/science/maths-school/maths-school-part-7/maths-school-part-7-concept-8)

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