Difference between revisions of "Pentagon"

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A '''pentagon''' is a [[polygon]] with 5 sides.
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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).
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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 $108^{\circ}$. The sum of the internal angles of any pentagon is $540^{\circ}$.

Construction

It is possible to construct a regular pentagon with compass and straightedge:

http://img164.imageshack.us/img164/1296/pentagonconstructiongt4.png

1. Draw circle $O$ (red).

2. Draw diameter $AB$ and construct a perpendicular radius through $O$.

3. Construct the midpoint of $CO$, and label it $E$.

4. Draw $AE$ (green).

5. Construct the angle bisector of $\angle AEO$, and label its intersection with $AB$ as $F$ (pink).

6. Construct a perpendicular to $AB$ at $F$.

7. Adjust your compass to length $AG$, and mark off points $H$, $I$ and $J$ on circle $O$.

8. $AGHIJ$ is a regular pentagon.

See also

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