Lines of Symmetry

Date: 01/29/2001 at 22:33:14
From: Laura
Subject: Polygons

How do you find how many lines of symmetry there are in a polygon  - 
for example, a square?  Is it the degrees that tell you?

Date: 01/29/2001 at 22:57:05
From: Doctor Rob
Subject: Re: Polygons

Thanks for writing to Ask Dr. Math, Laura.

For a *regular* polygon, the number of lines of symmetry is the
same as the number of sides.

For irregular polygons, the situation is more complicated.

Nonsquare rectangles have two.  
Nonsquare rhombuses have two.
Parallelograms that are neither rectangles nor rhombuses have none.  
Nonrhombus kites have one.  
Isosceles trapezoids have one.  
Nonisosceles trapezoids have none.  
Isosceles triangles have one.  
Triangles that are not isosceles have none.

- Doctor Rob, The Math Forum
  http://mathforum.org/dr.math/