Difference between revisions of "Pentagon"
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| − | + | In [[geometry]], a '''pentagon''' is a [[polygon]] with 5 sides. Each [[angle]] of a [[regular polygon | regular]] pentagon is <math>108^{\circ}</math>. The sum of the internal angles of any pentagon is <math>540^{\circ}</math>. | |
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| + | === Construction === | ||
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| + | It is possible to construct a regular pentagon with compass and straightedge: | ||
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| + | http://img164.imageshack.us/img164/1296/pentagonconstructiongt4.png | ||
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| + | 1. Draw circle <math>O</math> (red). | ||
| + | |||
| + | 2. Draw diameter <math>AB</math> and construct a perpendicular radius through <math>O</math>. | ||
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| + | 3. Construct the midpoint of <math>CO</math>, and label it <math>E</math>. | ||
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| + | 4. Draw <math>AE</math> (green). | ||
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| + | 5. Construct the angle bisector of <math>\angle AEO</math>, and label its intersection with <math>AB</math> as <math>F</math> (pink). | ||
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| + | 6. Construct a perpendicular to <math>AB</math> at <math>F</math>. | ||
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| + | 7. Adjust your compass to length <math>AG</math>, and mark off points <math>H</math>, <math>I</math> and <math>J</math> on circle <math>O</math>. | ||
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| + | 8. <math>AGHIJ</math> is a regular pentagon. | ||
== See also == | == See also == | ||
Revision as of 00:08, 6 May 2007
In geometry, a pentagon is a polygon with 5 sides. Each angle of a regular pentagon is 
. The sum of the internal angles of any pentagon is 
.
Construction
It is possible to construct a regular pentagon with compass and straightedge:
http://img164.imageshack.us/img164/1296/pentagonconstructiongt4.png
1. Draw circle 
(red).
2. Draw diameter 
and construct a perpendicular radius through .
3. Construct the midpoint of 
, and label it 
.
4. Draw 
(green).
5. Construct the angle bisector of 
, and label its intersection with as 
(pink).
6. Construct a perpendicular to at .
7. Adjust your compass to length 
, and mark off points 
, 
and 
on circle .
8. 
is a regular pentagon.
See also
This article is a stub. Help us out by expanding it.
