Construction step-by-step instructions :
Step 1: Find the midpoint of line segment AB. We will refer to this midpoint as point C. Also, extend line AB.
Step 2: Construct a circle with center B and radius BC. Label the intersection of circle B and line AB as point D.
Step 3: Construct a circle with a center at A and with radius AB, then construct a circle with a center at D and a radius of AD. Label the points of intersection of circles A and D with points E and F. (In order to save room, only part of circles A and D are shown below.)
Step 4: Construct line segment FE. Label the point where line segments FE and AB intersect with point G.
Step 5: Construct a circle with center at G and radius AG. Label the intersection of this circle and line segment AB with point H. Points G and H trisect line segment AB.
Click here for a GSP sketch to manipulate. (Requires GSP 4.0)
here for a verification of the construction.