Difference between revisions of "Pentagon"
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# <math>AGHIJ</math> is a regular pentagon. | # <math>AGHIJ</math> is a regular pentagon. | ||
− | ==The Golden Ratio | + | ==The Golden Ratio== |
− | The pentagon is closely associated with the | + | 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>. |
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== See Also == | == See Also == | ||
*[[Polygon]] | *[[Polygon]] | ||
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{{stub}} | {{stub}} |
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.