Segment trisection without compass I'm trying to figure out how to trisect a segment using only pen and ruler. There is a parallel line provided. No measurement is allowed.

lets mark ends of the segment as A and B.

* mark points C and D on the parallel line.
* draw lines BD and AC, mark the cross point as E
* draw lines BC and AD, mark the cross point as F
* draw line EF, mark its cross point with line CD as G
* draw line BG, mark its cross point with line AD as H



The line EH cuts segment AB in 2:1 ratio.