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Topic: Trapezoid definition
Replies: 26   Last Post: Oct 7, 2004 11:51 PM

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Mary Krimmel

Posts: 629
Registered: 12/3/04
Re: Is a rectangle a square?
Posted: Oct 29, 2003 3:56 PM
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At 03:43 PM 10/28/03 -0500, you wrote:

> > Is a square a rectangle? When did the geniuses of the Math world come
> > up with that one? If you refer to Webster, a square is a
> > parallelogram with 4 EQUAL sides and 4 right angles. Wouldn't that
> > rule out a rectangle? Sorry, but I'm no math wiz, just wondering why
> > my daughter got that answer wrong on a math quiz. Would love this
> > explained in Laymons Terms. :)

John Conway answered the question asked as the "subject" of the header.

Walter Whiteley gave what seems to me an excellent explanation in layman's

Adding my two cents may be more than you want or need, but here goes.

Yes, a square is a rectangle. I do not know just when math textbooks
undertook to make this clear, nor do I know at what level of math it is
explained. It would not surprise me to see kindergarten or preschool
teachers pointing to a shape saying "This is a square," and to another
shape saying "This is a rectangle." They are not wrong, but certainly their
methods lead to misconceptions that need to be set aside as students begin
to learn the way math "works".

The Webster's edition I use gives as definition for "square": "A rectangle
with four equal sides." American Heritage Dictionary's definition is
essentially the same: "A rectangle having four equal sides." Both
dictionaries define a rectangle as "a parallelogram with a right angle".
You did not tell whether you looked up "rectangle" in Webster, but I
suspect that if you do, you will see that by the definition you find there,
a square will be included as a rectangle. In any case, a parallelogram with
four equal sides and four right angles is a rectangle; "rectangle" is not
ruled out.

Check out your daughter's textbook, if she's using one. As Walter Whiteley
said, some elementary texts get this tangled up. Then if the teacher
doesn't make the situation clear, the student loses.

Best wishes for you and your daughter.

Mary Krimmel

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