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.
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. |