# Is a square a rectangle?

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I have noticed that the topics I am discussing is getting deeper and harder, so let me break the spell by this very elementary question:

Are squares rectangles?

Before we answer that question, we must know first what a rectangle looks like, and we must also know its properties.  Many doors and windows, for example, are in a shape of a rectangle. We can observe that a rectangle has the following characteristics:

1. It has four sides and four angles.
2. The measure of its interior angles is 90 degrees.
3. Opposite sides have the same lengths.
4. Opposite sides are parallel.

For those who have already learned about the parallel postulate, you will probably agree that some of the observations above can be derived from the other properties, but we will leave it that way, for it is not that relevant in the following discussion. Hmmm… I think I’m confused.

To say that an object is a rectangle, the four observations above must hold. Now, let us see if squares have the same properties as those mentioned above.

1. Do squares have four sides and four angles?
2. Do interior angles of a square measure 90 degrees?
3. Do opposite sides of a square have the same length?
4. Are opposite sides of a square parallel?

As we can see, the answers to the four questions above are all YES. Therefore, a square, inherits the properties of a rectangle. Therefore, a square is a rectangle.

It is clear, however, that a rectangle is not always a square.  For it to be a square, all its sides must have the same length.

Strictly speaking, if we look at the books, the definition of a rectangle is a quadrilateral whose all interior angles measure 90 degrees. Therefore, a square is a special rectangle.

Live Porcelain Doll by Vince Angoli
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