Constructing a square

This page shows how to construct (or draw) a square given the length of a side.

It starts with a given line segment AB. It then erects a perpendicular at one end of the line, which will become the second side of the square. The compass is then set to the length of the given side, and the other three sides are marked off.

Printable step-by-step instructions

The above animation is available as a printable step-by-step instruction sheet, which can be used for making handouts or when a computer is not available.


  Argument Reason
1 Angle ABC is 90° (a right angle) By construction. See Constructing a perpendicular to a line at a point for the proof.
2 Segments BC, CD and DA are the same length as AB They were all drawn with the same compass width - AB
3 Therefore ABCD is a square. Four congruent sides and interior angles are 90°

  - Q.E.D

Try it yourself

Click here for a printable construction worksheet containing two square constructions to try. When you get to the page, use the browser print command to print as many as you wish. The printed output is not copyright.

Other constructions pages on this site




Right triangles

Triangle Centers

Circles, Arcs and Ellipses


Non-Euclidean constructions