Are squares rectangles? Third grade math teacher told a student this was true. Grandmother needs confirmation on this!


Hi Nona,

I got the following response to your question from Claude.

This reminds me of a funny problem: "In a car, there are three women: two mothers and two daughters. How is this possible?" The answer is that in the car, there is a woman, her daughter, and her daughter's daughter. Daughters can also be mothers, though we sometimes forget it.

Now can a square also be called a rectangle? After all, why not? The square has all its angles right, so in my mind it fulfills all the required conditions to be called a rectangle; it doesn't matter that all its sides are equal.

Just to be on the safe side I checked in the Dictionary. Merriam-Webster gives the following definition of a rectangle:

Main Entry:
Pronunciation: 'rek-"ta[ng]-g&l
Function: noun
Etymology: Medieval Latin rectangulus having a right angle, from Latin rectus right +
angulus angle -- more at RIGHT, ANGLE
Date: 1571

: a parallelogram all of whose angles are right angles; especially : one with adjacent sides of unequal length

The "especially" seems to mean that the name is used more to describe the rectangles that are not squares, but it does not mean that the squares are not rectangles.


I think that the word "especially" in the dictionary definition illustrates a difference between words used in everyday language and words used in mathematics. In mathematics we can not have ambiguity in the technical language we use so we are very careful about how we define our terms. Not every mathematician, however, defines terms the same way. The current definition of a rectangle used by most authors is a parallelogram, all of whose angles are right angles and hence a square is a rectangle. Since the teacher says that a square is a rectangle I would conclude that this is the way the textbook defines a rectangle.


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