
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 stepbystep instructions
The above animation is available as a
printable stepbystep instruction sheet, which can be used for making handouts
or when a computer is not available.
Proof

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
Lines
Angles
Triangles
Right triangles
Triangle Centers
Circles, Arcs and Ellipses
Polygons
NonEuclidean constructions
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