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Bisecting a Line Segment with a Ruler Given a Parallel Line

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Suppose the segment lies on the line and that a line is parallel to .

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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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Contributed by: Izidor Hafner (August 2017)
Open content licensed under CC BY-NC-SA

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Details

The construction is valid by "The Trapezoid Theorem" [2, p. 73].

References

[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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