Bisecting a Line Segment with a Ruler Given a Parallel Line

Suppose the segment lies on the line and that a line is parallel to .
This Demonstration shows how to bisect using only a ruler.
1. Choose a point not on or .
2. Let the segments and intersect at points and , respectively.
3. Let the segments and intersect at point .
4. Then the line intersects at the midpoint of .


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The construction is valid by "The Trapezoid Theorem" [2, p. 73].
[1] B. I. Argunov and M. B. Balk, Elementary Geometry (in Russian), Moscow: Prosveščenie, 1966 p. 337.
[2] G. E. Martin, Geometric Constructions, New York: Springer, 1998.


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