Bizarre Trisection (V3) = GoGeometry Action 146!
Creation of this resource was inspired by a problem posted by Antonio Gutierrez (GoGeometry).  
Goal here is to TRISECT the segment shown below.
That is, our goal is to cut this segment into 3 congruent segments.  
  
Slide the slider slowly.  As you do, carefully observe what happens.  
You can move the 2 LARGE POINTS (segment endpoints) anywhere you'd like at any time.  
How can we formally prove why this method of segment trisection actually works?