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### Is a Square a Rectangle?

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

Hi,

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

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
shapes.

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
Check out our web site!  http://mathforum.org/dr.math/
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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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