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.
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.
|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.|