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Is a Square a Rectangle?

Date: 06/04/97 at 07:43:43
From: Kathy Harris
Subject: Elementary geometry

Dear Dr. Math,
We are studying geometric shapes in my second grade classroom. If you 
could answer this question in terms that they can understand, I would 
greatly appreciate it.  Is a square a rectangle?  Also, what is a 
pentagon?  In our studies we have found books with conflicting 
information and would like your ideas.

Thank you!
Kathy Harris

Date: 06/04/97 at 12:14:43
From: Doctor Ceeks
Subject: Re: Elementary geometry


The definitions of certain things in math sometimes become arbitrary 
and depend on conventions. Different people will feel different ways 
about things.

When there is conflicting information, it's okay to discuss things and 
try to come to some agreement within your class as to which 
definitions are the happiest ones to use.

My personal feeling on the questions you asked are as follows:

A square is a special kind of rectangle.  I like to consider the 
square as a special kind of rectangle because I've often had to refer 
to all shapes with four sides and four right angles as rectangles. If 
the rectangle were defined to not include the square, I would have to 
say "rectangles and squares" whenever I wanted to refer to such 
shapes. It's less cumbersome to allow "rectangle" to also refer to 
squares so I can simply say "rectangles" when I want to refer to such 

Also, of all rectangles, the one with four equal sides has the special 
property that all its sides are equal, and for this reason, has 
warranted a special name, "square".

Some people will want to disagree and not allow rectangle to include
squares because maybe when they say "rectangle" they really want 
people to think of something with a length and a width.  This is fine, 
if they want to think that way.  When I want to refer to a non-square 
rectangle, I might say "non-square rectangle" or "generic rectangle".

Anyway, the whole business is not really worth arguing about once it 
is seen that of all the four sided figures with four right angles, 
there is a special one which also has four equal sides.  That's worth 
noting, and once noted, it's time to move on to more important things.

A pentagon is generally agreed upon to be a five sided figure. When 
people want to refer to the special pentagon that has five equal sides 
and five equal angles, they say "regular pentagon".

-Doctor Ceeks,  The Math Forum
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Associated Topics:
Elementary Definitions
Elementary Geometry
Elementary Triangles and Other Polygons
Middle School Definitions
Middle School Geometry
Middle School Triangles and Other Polygons

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