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### Are Squares Rectangles? Are Rectangles Squares?

```Date: 03/29/2004 at 17:16:48
From: Alisa
Subject: Can a rectangle be a square

Can a rectangle be a square?  I just was wondering because a square
can be a rectangle, but can a rectangle be a square?

```

```
Date: 03/30/2004 at 09:01:48
From: Doctor Peterson
Subject: Re: Can a rectangle be a square

Hi, Alisa.

Actually, EVERY square is a rectangle, since the angles in a square
are always right angles.  That's more than saying that a square CAN be
a rectangle; it IS.

And since squares are rectangles, you know that some rectangles are
squares--namely, the squares are!

These ideas confuse many people.  It may help to think about other
categories, like dogs and animals.  Can a dog be an animal?  Of course
--every dog is an animal!  Can an animal be a dog?  Yes, if you look
at a dog, that is an animal that is a dog.  But not every animal is a

It sounds less silly with squares and rectangles, but the idea is the
same.  The trouble is that in everyday life, we usually use the word
"rectangle" to refer to non-squares, because if the shape were a
square, we would call it that.  So we teach children "this is a
rectangle, that is a square--the rectangle's sides are different
lengths".  But when you grow up, it's important to think of the square
as a SPECIAL rectangle, because it is all that a rectangle is, and
more.

It's as if someone looked at your dog and said, "What a fine animal
you've got!", and you answered, "That's not an animal--that's a
pedigreed Labrador Retriever."  The specific type of animal matters to
you, because it's special; but it really is still an animal too.  And
a square is still a rectangle--but it's not JUST a rectangle, it's a
(pedigreed) square.

If you have any further questions, feel free to write back.

- Doctor Peterson, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
Elementary Triangles and Other Polygons
Middle School Triangles and Other Polygons

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