Axes of Symmetry

Date: 2/3/96 at 0:13:8
From: Anonymous
Subject: Axes of symmetry

Can you give me guidance on how to explain axes of symmetry to a year 
5?  My son had some trouble with it and I'm not sure as a parent how 
to explain in an intuitive way.

Also, the correct answer to one question puzzled me a bit: a triangle 
was said to have three axes of symmetry, but it seems to me that this 
is only true for an equilateral triangle.  By the way, my basic 
definition of an axis of symmetry is that it joins points on the 
perimeter in such a way that it divides the figure into two identical 
figures.  I've checked the archives but couldn't find anything that 
seemed right for the level.

Thanks for any help you can give.

John Hannoush

Date: 10/1/96
From: Doctor Ceeks
Subject: Re: Axes of symmetry

Hi,

Symmetry is a very broad concept.

I might try to explain it like this.  Suppose you have an object,
like a triangle.  Suppose you're with a friend, and the friend leaves
the room for the moment.  While your friend is gone, you do something
to the object... you move it, flip it, spin it, or something, in such
a way that when your friend comes back, your friend can't tell the
difference and has no idea you did something to the object.

Then you've discovered a symmetry of the object.

Now, if you rotated the object about an axis (like the earth spins
on an axis), then there's an "axis of symmetry."

For an equilateral triangle, there are four axes of symmetry, three
in the plane of the triangle, and one that is perpendicular to
the plane through the center of the triangle (120- or 240-degree 
rotation).

-Doctor Ceeks,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/