Trisection of a line segment

In today's proof without words series, let's take a look at how the trisection of any straight line segment can be achieved by using compass and straightedge (ruler without markings) construction. You will see that we make good use of the property of the centroid of triangle, which divides each of the medians in a lengths of ratio 2:1. This useful geometrical fact will come in handy for tackling other geometry problems as well. Diagrams are taken from 'Proofs without Words- Exercises in Visual Thinking' by Roger Nelson of Mathematical Association of America.