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 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.

## 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.
While you are here..

... I have a small favor to ask. Over the years we have used advertising to support the site so it can remain free for everyone. However, advertising revenue is falling and I have always hated the ads. So, would you go to Patreon and become a patron of the site? When we reach the goal I will remove all advertising from the site.

It only takes a minute and any amount would be greatly appreciated. Thank you for considering it!   – John Page

Become a patron of the site at   patreon.com/mathopenref