Trisecting a Line SegmentDate: 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/ |
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