   SEARCH HOME Math Central Quandaries & Queries  Question from a parent: Why is a square a rectangle but a rectangle is not a square? Explain your answer. There are many equivalent definitions of a square and a rectangle. I am going to use

Rectangle:
A rectangle is a quadrilateral with 4 right angles.

Square:
A square is a quadrilateral with 4 sides of equal length and 4 right angles.

We have responded to this question many times before and I think that part of the confusion is the way the question is worded. I think it would be more clear if the question was worded

Why is every square a rectangle but not every rectangle is a square?

Suppose you have a square, any square at all. From the definition above this square is a quadrilateral with 4 sides of equal length and 4 right angles. Does this square satisfy the conditions in the definition of a rectangle? If so it is a rectangle.

To show that not every rectangle is a square you need to find a rectangle that is not a square.

I hope this helps.
Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.