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Is a square a rectangle?

Is a square a rectangle?

Author: Christopher Danielson

To demonstrate that squares are special rectangles.

Through the use of two videos, a critical eye is cast on the relationship between squares and rectangles.

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The answer to the question in the title of this packet is "yes!"

Squares are rectangles, although not all rectangles are squares.

There are several ways to define a rectangle. Let's use this definition from Wikipedia:

A rectangle is any quadrilateral with four right angles.

ANY quadrilateral. Even one with all sides the same length.

But ask around. People tend to think of them as different from each other. Why? Let's see...


So why do people think squares are not rectangles?

Because the marmot told them so (or at least implied it).

Because our minds want to sort things into discrete categories. We think, "This shape goes in the 'rectangle' box OR the 'square' box."

But in mathematics, we are often concerned with boxes inside boxes. The square box is inside the rectangle box, so when we throw a figure into the square box, it is automatically in the rectangle box too.

Squares ARE rectangles; they're just special ones.

THANKS to my students for ferreting out these and many other extracurricular geometry resources (esp. Lindsey and Betsy for finding these two videos).