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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 

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 

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. 

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

taken from article by Tad Watanabe in thread   

-Doctor Steve,  The Math Forum
 Check out our web site!   
Associated Topics:
Elementary Definitions
Elementary Geometry
Elementary Triangles and Other Polygons
High School Definitions
High School Geometry
High School Triangles and Other Polygons
Middle School Definitions
Middle School Geometry
Middle School Triangles and Other Polygons

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