Constructing an Equilateral Triangle
This demonstration shows how to draw an equilateral triangle of a given side, using only a compass and straightedge. See "Introduction to Euclidean Constructions".

We start with a segment AB which defines the length of the side of the desired triangle. The result is an equilateral triangle PQR, the length of whose sides is equal to AB. For more information, see Definition and properties of an Equilateral Triangle.
This procedure is also useful for creating a 60° angle - the internal angle of all equilateral triangles.
Instructions Click on 'Next' to go through the construction one step at a time, or click on 'Run' to let it run without stopping.
(If there is no image below, see support page.)

Step-by-step Instructions
Step 1 Pick a point P that will be one vertex of the finished triangle.
Step 2 Place the point of the compass on the point A and set it's drawing end to point B. The compass is now set to the length of the sides of the finished triangle. Do not change it from now on.
Step 3 With the compass point on P, make two arcs, each roughly where the other two vertices of the triangle will be.
Step 4 On one of the arcs, mark a point Q that will be a second vertex of the triangle. It does not matter which arc you pick, or where on the arc you draw the point.
Step 5 Place the compass point on Q and draw an arc that crosses the other arc, creating point R.
Step 6 Using the straightedge, draw three lines linking the points P,Q and R.
Step 7 Done. The triangle PQR is an equilateral triangle. Its side length is equal to the distance AB.
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

Lines

Angles

Triangles

Triangle Centers

Circles, Arcs and Ellipses

Non-Euclidean constructions