Pentagon
From AoPSWiki
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.
See Also
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