Quadrilateral Classification: Definition of a Trapezoid

Date: 01/15/97 at 13:45:54
From: Anonymous
Subject: Trapezoid ?

Dr. Math,
     
What is the correct definition for a trapezoid?  And why?
     
My questions come from the Math Department at Carroll Middle School 
in SouthLake, Texas.  Two of the math teachers have found well-known 
publications with very different definitions for a Trapezoid.
     
1) Trapezoid: Quadrilateral with at least 1 pair of sides parallel.
     
2) Trapezoid: A trapezoid is a quadrilateral with exactly one pair of 
   parallel sides.
     
Can you help? Thanks.
     
- Craig C.

Date: 01/15/97 at 15:48:19
From: Doctor Steve
Subject: Re: Trapezoid ?

Hello Craig,

This has actually been discussed quite thoroughly by professionals on 
our geometry newsgroups. You can search for these discussions by going 
to 

  http://mathforum.org/kb/forum.jspa?forumID=128   

and searching for the word  trapezoid . In the list of found 
discussions you'll see three that most relate: Definition of a 
trapezoid, Classification of Quadilaterals, and Defining 
Quadilaterals.

The bottom line is that these professionals are most comfortable with 
a definition like the first one you offer.

Here is a classification scheme that reflects the first definition, 
found in "A Problem Solving Approach to Mathematics for Elementary 
School Teachers" by Billstein et al. 

                      Quadrilateral
                      /           \
                    /               \
              Kite                    Trapezoid
               |                      /       \
               |                    /          \
               |              Parallelogram   Isosceles
               |              /       \       Trapezoid
               |            /           \       /
               \          /               \   /
                 Rhombus                  Rectangle
                      \                  /
                        \             /
                          \        /
                           Square

taken from article by Tad Watanabe in thread

 http://mathforum.org/kb/message.jspa?messageID=1076714   

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