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How to Name a Polygon by Vertices

Date: 06/30/2004 at 19:26:23
From: Claudia
Subject: variable naming convention

Is there a specific convention for naming the vertices of polygons?  
For example, picture a triangle with vertices at R (0, 0), S (0, 3),
and T (4, 0).  Would you call this triangle RST or RTS? 

In other words, is the figure named by going clockwise or counter-
clockwise?  How do you determine the first vertex named?  Are there 
ever exceptions?



Date: 06/30/2004 at 23:06:50
From: Doctor Peterson
Subject: Re: variable naming convention

Hi, Claudia.

A triangle can be named in any order at all; a polygon in general can 
be named by starting at any point and going either clockwise or 
counterclockwise.

There is good reason for this.  In many cases we don't care about the 
direction or the starting point; it makes no difference in most 
theorems.  Usually we don't even know the direction of the points; 
that is not one of the facts given in the statement of the theorem. 
And perhaps most important, we need to be able to say in a figure 
like this

         A
        /|\
       / | \
      /  |  \
     /   |   \
    /    |    \
   C-----B-----D

that triangles ABC and ABD are congruent; but if we had to name 
triangles in a certain order, then one of these two names would be 
illegal, since if one is clockwise then the other has to be 
counterclockwise!

So don't worry about consistency.  In fact, if you are teaching, you 
should deliberately name triangles in different orders, to get 
students used to the fact that naming does not imply anything about 
orientation.

If you have any further questions, feel free to write back.

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/ 
Associated Topics:
High School Triangles and Other Polygons

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