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Trisecting a Line

Date: 11/03/97 at 17:38:08
From: megan federow
Subject: Trisecting a line

How would you trisect a line using a compass and a straight edge?  
I tried with circles but i don't know if that is right. Could you help 
me?  Thanks.

Date: 11/03/97 at 19:21:33
From: Doctor Tom
Subject: Re: Trisecting a line

Hi Megan,

The usual construction is this:

Draw another line that goes through one of the endpoints of the
segment that you're trying to trisect. In reality, it can be any 
line, but it works best if it makes a relatively small angle (say 
30 degrees) with the original segment.

Next, open your compass to any size (but it works better if the
size is roughly 1/3 of the size of the segment you're trying to
trisect). Put the point of the compass on the intersection of the 
segment and your new line, and make a mark on the new line with the 
pencil on the compass. Now put the point of the compass at that new 
mark (without changing the opening), and mark another point on the new 
line. Do it again, and you'll have three equal-sized segments marked 
off on the new line.

From the final mark, draw a line to the other end of the segment
you're trying to trisect. Then construct lines parallel to that one 
going through the other two new points on the line. These three 
parallel lines will trisect the original segment.

This would sure be easier to explain with a drawing!

-Doctor Tom,  The Math Forum
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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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