Difference between revisions of "Pentagon"
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== Construction == | == Construction == | ||
| − | + | [[Image:Pentagon.png|center]] | |
It is possible to construct a regular pentagon with compass and straightedge: | It is possible to construct a regular pentagon with compass and straightedge: | ||
| − | + | # Draw circle <math>O</math> (red). | |
| − | + | # Draw diameter <math>AB</math> and construct a perpendicular radius through <math>O</math>. | |
| − | + | # Construct the midpoint of <math>CO</math>, and label it <math>E</math>. | |
| − | + | # Draw <math>AE</math> (green). | |
| − | + | # Construct the angle bisector of <math>\angle AEO</math>, and label its intersection with <math>AB</math> as <math>F</math> (pink). | |
| − | + | # Construct a perpendicular to <math>AB</math> at <math>F</math>. | |
| − | + | # 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>. | |
| − | + | # <math>AGHIJ</math> is a regular pentagon. | |
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== See also == | == See also == | ||
*[[Polygon]] | *[[Polygon]] | ||
| + | {{stub}} | ||
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| + | [[Category:Definition]] | ||
[[Category:Geometry]] | [[Category:Geometry]] | ||
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Revision as of 15:38, 25 December 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:
- Draw circle
(red). - Draw diameter
and construct a perpendicular radius through . - Construct the midpoint of
, and label it 
. - Draw
(green). - Construct the angle bisector of
, and label its intersection with as 
(pink). - Construct a perpendicular to at .
- Adjust your compass to length
, and mark off points 
, 
and 
on circle . 
is a regular pentagon.
(red).
and construct a perpendicular radius through 
, and label it 
.
(green).
, and label its intersection with 
(pink).
, and mark off points 
, 
and 
on circle 
is a regular pentagon.See also
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