---
title: "Ruler and compass constructions"
description: "Use ruler and compasses to perform standard constructions: perpendicular bisector of a line segment, perpendicular to a line from or at a given point, and bisecting an angle"
canonical: https://lightmysky.com/learn/mathematics/ruler-and-compass-constructions-mt_ZrsqGVG-Wt
source: https://lightmysky.com/learn/mathematics/ruler-and-compass-constructions-mt_ZrsqGVG-Wt.md
retrieved: 2026-09-02
---

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# Ruler and compass constructions

Use ruler and compasses to perform standard constructions: perpendicular bisector of a line segment, perpendicular to a line from or at a given point, and bisecting an angle

Subject: Mathematics · Area: Geometry · Ages 12 to 14
Page: https://lightmysky.com/learn/mathematics/ruler-and-compass-constructions-mt_ZrsqGVG-Wt

## Ready when they can

- Construct the perpendicular bisector of a line segment using compasses and a straight edge
- Construct an angle bisector and verify by measuring both halves
- Construct a perpendicular from a point to a line using compasses only

## Lesson: Constructing with a ruler and compasses

A construction is a drawing made with only two tools: a ruler as a straight edge, and a pair of compasses. You never use a protractor. Every construction works because a compass draws every point that sits the same distance from one center point.

*(drawing: A compass holds one width, so every point it draws sits the same distance from the center. That one fact powers every construction here.)*

**Example.** To bisect segment AB exactly in half: open your compasses wider than half of AB. Put the point on A and draw an arc above and below the line. Keep the same width, put the point on B, and draw two more arcs that cross the first ones. Draw a straight line through the two crossing points. That line is the perpendicular bisector: it cuts AB in half at a right angle.

**Example.** To drop a perpendicular from point P to a line: put the compass point on P and draw an arc that crosses the line at two spots. From each of those spots, draw an arc below the line, keeping the same width. Where those two arcs cross, draw a line back to P. That line meets the original line at exactly 90 degrees.

**Example.** To bisect an angle at point O: put the compass point on O and draw an arc that crosses both arms. Keeping the same width, put the point on each crossing spot and draw two more arcs that meet inside the angle. Draw a line from O through that meeting point. It splits the angle into two equal halves.

**Tip.** Keep your compass width exactly the same for both arcs in one step. If you widen or narrow it partway through, the arcs will not cross where they should, and the construction comes out wrong.

**Recap.** Same compass width, two crossing arcs, then a straight line through the crossing point: that is how you build an exact half or a true right angle without ever using a protractor.

## Practice

8 questions on this page, each with its working shown.

## Needs first

- [Accurate drawing and scale diagrams](https://lightmysky.com/learn/mathematics/accurate-drawing-and-scale-diagrams-mt_Jf8xcX4UTq)

## Opens up

- [Trigonometry basics](https://lightmysky.com/learn/mathematics/trigonometry-basics-mt_KB_Czd7RQH)