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Constructing a triangle given three sides (SSS)

This is the step-by-step, printable version. If you PRINT this page, any ads will not be printed.

See also the animated version.

After doing this Your work should look like this
Start with three line segments that will be the three sides of the triangle ABC. Geometry construction with compass and straightedge or ruler or ruler
1.  Mark a point A that will be one vertex of the new triangle. Geometry construction with compass and straightedge or ruler or ruler
2.  Set the compasses' width to the length of the segment AB. This will become the base of the new triangle. Geometry construction with compass and straightedge or ruler or ruler
3.  With the compasses' point on A, make an arc near the future vertex B of the triangle. Geometry construction with compass and straightedge or ruler or ruler
4.  Mark a point B on this arc. This will become the next vertex of the new triangle. Geometry construction with compass and straightedge or ruler or ruler
5.  Set the compasses' width to the length of the line segment AC. Geometry construction with compass and straightedge or ruler or ruler
6.  Place the compasses' point on A and make an arc in the vicinity of where the third vertex of the triangle (C) will be. All points along this arc are the distance AC from A, but we do not yet quite know exactly where the vertex C is. Geometry construction with compass and straightedge or ruler or ruler
7.  Use the compasses to measure the length of the segment BC, the length of the third side of the triangle. Geometry construction with compass and straightedge or ruler or ruler
8.  From point B, draw an arc crossing the first. Where these intersect is the vertex C of the triangle Geometry construction with compass and straightedge or ruler or ruler
9.  Finally, draw the three sides AB, AC, and BC of the new triangle. Geometry construction with compass and straightedge or ruler or ruler
10.  Done. The blue triangle ABC has each side congruent to the the corresponding line segment. Geometry construction with compass and straightedge or ruler or ruler

Other constructions pages on this site

Lines

Angles

Triangles

Right triangles

Triangle Centers

Circles, Arcs and Ellipses

Polygons

Non-Euclidean constructions