Pentagon
In geometry, a pentagon is a polygon with 5 sides. The sum of the internal angles of any pentagon is 
. Each angle of a regular 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 and the Pentagram
The regular pentagon is closely associated with the Golden Ratio. More specifically, the ratio of a diagonal to an edge is 
.
By drawing each of the diagonals, one can form a pentagram, or five-pointed star, in which each of the internal angles is 
.
See Also
This article is a stub. Help us out by expanding it.
