Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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

 Messages: [ Previous | Next ]
 Walter Whiteley Posts: 418 Registered: 12/3/04
Re: Is a rectangle a square?
Posted: Oct 28, 2003 3:43 PM

This is a 'standard' difficulty, and some elementary math
texts get this tangled up.

The way mathematicians work, think, and use these words,
we are 'inclusive'. So something with four Equal sides
DOES have two pairs of opposite sides equal.
That means is also a rectangle.

Look at it in reverse.

If you give some definition of a rectangle:
eg. four right angles, then you can start to look
at figures which have this property.

When you happen to find an example with four
equal angles, you will agree it is a rectangle, even
before you check whether the sides are ALSO equal.
If the sides are also equal, it is still a rectangle and is
also a square. The 'image' of this is a collection of
all rectangles as a big circle, and the collection of
all squares as a smaller circle INCLUDED inside the bigger
one.

Take numbers. We can have all even numbers. We can
have all numbers divisible by 10. The second collection
is 'included' in the set of even numbers. They did not stop
being even, they just picked up an extra additional property.

Does that help?

Walter Whiteley

Pamela Paramour 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. :)

Date Subject Author
8/7/00 John Benson
8/8/00 John Conway
8/8/00 Floor van Lamoen
8/8/00 John Conway
8/9/00 Floor van Lamoen
8/9/00 mary krimmel
8/9/00 Lee Rudolph
10/17/02 Julio Albornoz
10/18/02 Walter Whiteley
10/18/02 G.E. Ivey
10/28/03 Pamela Paramour
10/28/03 Walter Whiteley
10/28/03 John Conway
10/29/03 Mary Krimmel
10/29/03 John Conway
10/30/03 Rick Nungester
9/28/04 Kit
9/28/04 David W. Cantrell
9/28/04 NealAgMan@nyc.rr.com
9/28/04 Mary Krimmel
10/7/04 Donna W.
10/7/04 Donna W.
10/23/02 Ken.Pledger@vuw.ac.nz
10/25/02 Pat ballew
8/9/00 Jon Marshall
8/9/00 Floor van Lamoen
8/10/00 John Conway