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### Is a Square a Rhombus?

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Date: 8/30/96 at 13:17:5
From: Carol Boyer
Subject: Is a Square a Rhombus?

My son is in fourth grade, and his homework had a list of geometric
shapes and he was to say whether each was a rhombus or not.  Next to
"square", he had written "yes."  I told him that a square was not a
rhombus, but he insists that his teacher said that it was.

Well, I have checked three different dictionaries and am coming up
with some conflicting information. They all agree that a rhombus is an
equilateral parallelogram, but one says the angles are oblique, one
says the angles are USUALLY oblique (implying that they don't have to
be), and one specifically says the angles are NOT right angles.

So, what's the official word?  Is a square a rhombus or not?
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Date: 8/30/96 at 13:43:28
From: Doctor Jodi
Subject: Re: Is a square a rhombus?

Hi Carol!

Eric's online treasure trove of math defines a rhombus as:

A quadrilateral with both pairs of opposite sides parallel (and
therefore of the same length), i.e. an equilateral parallelogram.

According to this definition, a square is a rhombus.  Thanks for
your question - it's a good one!

-Doctor Jodi,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
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Associated Topics:
Elementary Definitions
Elementary Geometry
Elementary Triangles and Other Polygons

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