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.
|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,