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. | ||
− | + | ==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 == | |
+ | *[[Polygon]] | ||
− | + | {{stub}} | |
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+ | [[Category:Definition]] | ||
[[Category:Geometry]] | [[Category:Geometry]] | ||
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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.
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.