
Constructing an Equilateral Triangle
Geometry construction using a compass and straightedge
This page shows how to construct an
equilateral triangle
with compass and straightedge or ruler. An equilateral triangle is one with all three sides the same length. It begins with a given
line segment
which is the length of each side of the desired equilateral triangle.
It works because the compass width is not changed between drawing each side, guaranteeing they are all
congruent
(same length). It is similar to the
60 degree angle construction, because the
interior angles
of an equilateral triangle are all 60 degrees.
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
The image below is the final drawing above.

Argument 
Reason 
1 
PQ, PR and QR are all
congruent to AB and so all have the same length 
Compass width set from AB used to draw them all 
2 
Triangle RPQ is an equilateral triangle with the given side length AB. 
All three sides congruent.
See Equilateral triangle definition. 
 Q.E.D
Try it yourself
Click here for a printable worksheet containing an ellipse drawing problem.
When you get to the page, use the browser print command to print as many as you wish. The printed output is not copyright.
Try it yourself
Click here for a printable worksheet containing two problems 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
(C) 2009 Copyright Math Open Reference. All rights reserved

