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. |

- Q.E.D

- Introduction to constructions
- Copy a line segment
- Sum of n line segments
- Difference of two line segments
- Perpendicular bisector of a line segment
- Perpendicular from a line at a point
- Perpendicular from a line through a point
- Perpendicular from endpoint of a ray
- Divide a segment into n equal parts
- Parallel line through a point (angle copy)
- Parallel line through a point (rhombus)
- Parallel line through a point (translation)

- Bisecting an angle
- Copy an angle
- Construct a 30° angle
- Construct a 45° angle
- Construct a 60° angle
- Construct a 90° angle (right angle)
- Sum of n angles
- Difference of two angles
- Supplementary angle
- Complementary angle
- Constructing 75° 105° 120° 135° 150° angles and more

- Copy a triangle
- Isosceles triangle, given base and side
- Isosceles triangle, given base and altitude
- Isosceles triangle, given leg and apex angle
- Equilateral triangle
- 30-60-90 triangle, given the hypotenuse
- Triangle, given 3 sides (sss)
- Triangle, given one side and adjacent angles (asa)
- Triangle, given two angles and non-included side (aas)
- Triangle, given two sides and included angle (sas)
- Triangle medians
- Triangle midsegment
- Triangle altitude
- Triangle altitude (outside case)

- Right Triangle, given one leg and hypotenuse (HL)
- Right Triangle, given both legs (LL)
- Right Triangle, given hypotenuse and one angle (HA)
- Right Triangle, given one leg and one angle (LA)

- Finding the center of a circle
- Circle given 3 points
- Tangent at a point on the circle
- Tangents through an external point
- Tangents to two circles (external)
- Tangents to two circles (internal)
- Incircle of a triangle
- Focus points of a given ellipse
- Circumcircle of a triangle

- Square given one side
- Square inscribed in a circle
- Hexagon given one side
- Hexagon inscribed in a given circle
- Pentagon inscribed in a given circle

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