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.
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.
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. |