Sum of line segments
Geometry construction using a compass and straightedge

This construction shows how to create a line segment whose length is the sum of a set of given segments (here three). It will work with any number of given segments. See also Difference of two segments.

Printable step-by-step instructions

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 proof of this construction is trivial. This is the same drawing as the last step in the above animation.

  Argument Reason
1 The segment PR is congruent to the given segment a Copied using the procedure in Copying a line segment. See that page for proof.
2 The segment RS is congruent to the given segment b See (1)
3 The segment SQ is congruent to the given segment c See (1).
4 PQ is the sum of given segments a,b,c From (1), (2), (3). All segments are colinear and adjacent.

  - Q.E.D

Try it yourself

Click here for a printable worksheet containing two line segment copying problems. When you get to the page, use the browser print command to print as many as you wish. The printed output is not copyright.
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Other constructions pages on this site




Right triangles

Triangle Centers

Circles, Arcs and Ellipses


Non-Euclidean constructions