Draw any ray with endpoint A, but not containing segment AB.

Then, mark off three congruent segments of any length on the ray as illustrated in the picture below. For a more detailed explanation of how to use circles and the radii of circles to construct equal segments, see the GSP trisecting a line segment script file.

Draw segment BE and construct angles at D and C that are congruent to angle AEB. Using these angles, draw lines through C and D that intersect the circles as shown below. You may also construct lines parallel to segment BE to obtain the trisection. Open the GSP sketch by clicking here to further investigate the trisection of a line segment.

To better observe the trisection, hide all of the construction items as shown below.