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Determine whether the following statement is true or false: a rectangle is a square.
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It might be useful here to begin by recalling the mathematical definition of a rectangle.
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A rectangle is a four-sided polygon, or quadrilateral, where all interior angles are 90 degrees.
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So, we could draw a rectangle that looks like this.
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It’s got a length and width of six and four, but all the interior angles are 90 degrees.
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We could draw a different rectangle that looks like this, like this, or even like this.
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The important thing is that each of these rectangles that we’ve drawn have interior angles of 90 degrees.
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So, now, let’s look at the definition of a square.
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This is a four-sided polygon with all sides equal and all interior angles are 90 degrees.
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So, let’s look at the rectangles we’ve drawn and see if any of these fit to the definition of a square.
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In this first example, we do not have all sides equal, even though all the interior angles are 90 degrees.
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So, this would not be a square.
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In the second diagram, we do not have all sides equal.
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So, this one is not a square, neither is the third diagram that we’ve drawn.
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In the last diagram, however, we do have a square because we have all the sides equal and all interior angles are 90 degrees.
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So, to answer the question “is a rectangle a square,” we would have to say no, as there’s only one time when this occurs, whenever all the sides are equal.
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Because we found a number of examples where a rectangle is not a square, then we have to give the answer that this is false.
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To further illustrate this, if we were to draw a Venn diagram of rectangles and squares, then the region of squares would fit within the rectangles.
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We could interpret this by saying that all squares are rectangles, but not all rectangles are squares.