Is a Square a Rectangle?

Today is the day that you finally learn the answer to the controversial question as to whether or not a square can be a rectangle. Before we explore the definitive answer to this question, let’s take a look at two very important definitions:

What is a Square?

A square is a closed figure with four sides of equal lengths and four right angles.

What is a Rectangle?

A rectangle is a closed figure with four straight sides and four right angles.

The subtle difference in definitions between a square and a rectangle is extremely important. Why? Because this subtle difference is the key to determining whether or not a square is a rectangle.

So, is a square a rectangle?

The quick answer is YES! A square can be a rectangle by definition.

Now let’s explore the reasons why a square is always a rectangle by using an analogy to cookies that will make the answer very simple!

All squares are rectangles, but not all rectangles are squares (just like all Oreos are cookies, but not all cookies are Oreos).

The Cookie Analogy

By definition, a cookie is a small baked treat that is typically round, flat, and crisp.

And we all know that an Oreo is a type of cookie (and certainly fits this definition).

But, is every cookie an Oreo?

Definitely not! An Oreo is a special type of cookie, but there are lots of other types of cookies including sugar cookies, chocolate chip cookies, girl scout cookies, and gingerbread cookies.

And furthermore, we can conclude that:

An Oreo is a special kind of cookie.
Every Oreo is a cookie, but not every cookie is an Oreo.

Now let’s extend this same exact type of thinking from the cookie analogy to understand why a square is a rectangle.

Every Square is a Rectangle. Here’s Why:

Remember that a rectangle is a closed figure with four straight sides and four right angles.

Does a Square fit this definition? YES! A square is a special kind of closed figure with four straight sides and four right angles that also has sides that all have equal length.

Therefore, we can conclude that:

A Square is a special kind of rectangle.
Every Square is a rectangle, but not every rectangle is a square.

Conclusion: a square is always a rectangle, but a rectangle is not always a square.

However, it is important to keep in mind that even though all squares are rectangles, not all rectangles are squares. Just like in the cookie example, all Oreos are cookies, but not all cookies are Oreos. And the same is true with squares and rectangles. So, while all squares are rectangles, not all rectangles are squares.

Do you want to learn more about why all squares are rectangles? Check out our Is a Square a Rectangle? YouTube video that accompanies this post:

We Spent All Morning Working On This Rectangle Math Puzzle. Can You Solve It?

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