Recently, I discovered a way to reflect a line, specifically the top base of a trapezoid to the bottom base of a trapezoid. This is done by taking the diagonals and the median (The segment that connects between the midpoints of the sides), and then drawing lines from the top vertices to the intersection of the diagonals and the median. At the point of where those to new lines intersect the bottom base, a exact reflection of the top base is formed on either side of the bottom base. A good application of this is to have the top base be 1/3 or 2/3 the length of the bottom base, by then trisecting it.
About this, I had two questions.
1) If somebody else has found this. 2) If it can be proved.