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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
.
Contributed by:
Izidor Hafner
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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.
RELATED LINKS
Trapezoid
(
Wolfram
MathWorld
)
PERMANENT CITATION
Izidor Hafner
"
Bisecting a Line Segment with a Ruler Given a Parallel Line
"
http://demonstrations.wolfram.com/BisectingALineSegmentWithARulerGivenAParallelLine/
Wolfram Demonstrations Project
Published: August 4, 2017
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