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>. | 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>. | ||
| − | + | == 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. | ||
| − | + | ==The Golden Ratio== | |
| + | The pentagon is closely associated with the [[Golden Ratio]]. More specifically, the ratio of a diagonal to an edge is <math>\frac{1+\sqrt{5}}{2}</math>. | ||
| − | + | == See Also == | |
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| − | == See | ||
*[[Polygon]] | *[[Polygon]] | ||
{{stub}} | {{stub}} | ||
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| + | [[Category:Definition]] | ||
| + | [[Category:Geometry]] | ||
Latest revision as of 08:59, 6 June 2022
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.The Golden Ratio
The pentagon is closely associated with the Golden Ratio. More specifically, the ratio of a diagonal to an edge is 
.
See Also
This article is a stub. Help us out by expanding it.
