Associated Topics || Dr. Math Home || Search Dr. Math

### Symmetry Lines

```
Date: 03/30/2000 at 19:29:54
From: Ian
Subject: Symmetry lines

How many symmetry lines are in a circle?
```

```
Date: 03/31/2000 at 18:13:58
From: Doctor Ian
Subject: Re: Symmetry lines

Hi Ian,

I assume that you already understand that a line of symmetry is a line
that divides a figure into two similar parts.

Think about a circular clock. A line that goes through the 12 and the
6 cuts the clock into two similar pieces, so that's one line of
symmetry.

A line that goes through the 1 and the 7 is also a line of symmetry.

Is there at least one other line of symmetry between those two lines?
Yes, the one that goes through the point halfway between the 12 and
the 1, and the point halfway between the 6 and the 7. Draw a picture
and convince yourself that this is true.

In fact, no matter how close together two lines of symmetry are, there
will always be another one halfway between them.

So if you ever _thought_ that you'd counted _all_ the lines of
symmetry, there would always be at least one more that you hadn't
counted yet.

What does that tell you about the number of lines of symmetry in a
circle?

- Doctor Ian, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Conic Sections/Circles
High School Geometry
High School Symmetry/Tessellations
Middle School Conic Sections/Circles
Middle School Geometry

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search