During AMC testing, the AoPS Wiki is in read-only mode. No edits can be made.

Difference between revisions of "Pentagon"

m
Line 1: Line 1:
 
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 ===
+
== Construction ==
  
 
It is possible to construct a regular pentagon with compass and straightedge:
 
It is possible to construct a regular pentagon with compass and straightedge:

Revision as of 23:08, 5 May 2007

In geometry, a pentagon is a polygon with 5 sides. Each angle of a regular pentagon is $108^{\circ}$. The sum of the internal angles of any pentagon is $540^{\circ}$.

Construction

It is possible to construct a regular pentagon with compass and straightedge:

http://img164.imageshack.us/img164/1296/pentagonconstructiongt4.png

1. Draw circle $O$ (red).

2. Draw diameter $AB$ and construct a perpendicular radius through $O$.

3. Construct the midpoint of $CO$, and label it $E$.

4. Draw $AE$ (green).

5. Construct the angle bisector of $\angle AEO$, and label its intersection with $AB$ as $F$ (pink).

6. Construct a perpendicular to $AB$ at $F$.

7. Adjust your compass to length $AG$, and mark off points $H$, $I$ and $J$ on circle $O$.

8. $AGHIJ$ is a regular pentagon.

See also

This article is a stub. Help us out by expanding it.

Invalid username
Login to AoPS