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### Trisecting a Line Segment

Date: 08/13/99 at 05:40:34
From: cbr53530
Subject: Geometry Constructions

I have a question on a geometry construction that I hope you can help
me solve. How can I measure one-third of a line of an unknown length
using a compass and a straightedge?

Date: 08/13/99 at 11:51:58
From: Doctor Rob
Subject: Re: Geometry Constructions

Thanks for writing to Ask Dr. Math.

Start with the given line segment AB. At A, draw a new line through A
not coinciding with AB. Using any convenient length, mark off points C
and D on that line such that AC = CD.

Through B, draw a line parallel to AD.  On this line, using the same
length as before, mark off points E and F such that BE = EF = AC = CD,
and E and F are on opposite sides of line AB from points C and D.

Connect CF and DE. Those two lines will cut AB into equal thirds.

Diagram:

/
D o.
/  `.
/     `.
C o.       `.
/  `.       `.
/     `.       `.
A o--------+---------+--------o B
`.       `.     /
`.       `.  /
`.       `o E
`.     /
`.  /
`o F
/

- Doctor Rob, The Math Forum
http://mathforum.org/dr.math/

Associated Topics:
High School Constructions
High School Euclidean/Plane Geometry
High School Geometry
Middle School Geometry
Middle School Two-Dimensional Geometry

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