This page shows how to construct a triangle given the length of all three sides, with compass and straightedge or ruler. It works by first copying one of the line segments to form one side of the triangle. Then it finds the third vertex from where two arcs intersect at the given distance from each end of it.

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 with the red items added.

Argument | Reason | |
---|---|---|

1 | Line segment LM is congruent to AB. | Drawn with the same compass width. See Copying a line segment |

2 | The third vertex N of the triangle must lie somewhere on arc P. | All points on arc P are distance AC from L since the arc was drawn with the compass width set to AC. |

3 | The third vertex N of the triangle must lie somewhere on arc Q. | All points on arc Q are distance BC from M since the arc was drawn with the compass width set to BC. |

4 | The third vertex N must lie where the two arcs intersect | Only point that satisfies 2 and 3. |

5 | Triangle LMN satisfies the three side lengths given.
LM is congruent to AB, LN is congruent to AC, MN is congruent to BC, |

- 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 at a point on a line
- 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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