__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)**

**Click
here for a verification of the construction****.**