Is a square with a diagonal drawn connecting two corners still considered a square? This is a question about the definition of a square.
Is a square with a diagonal drawn connecting two corners still considered a square?
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$\begingroup$
geometry
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2I would say it's a *dissected* square... – 2012-07-28
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0Yes, but why are you asking? Is this yet another item where you were marked wrong by your instructor and you want us to say you were right? – 2012-07-28
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4Is a person wearing only a hat nude? Depends on what one is concentrating on. – 2012-07-28
1 Answers
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No, a square is a 4 sided polygon, with all sides equal, and all interior angles 90 degrees.
A square with a line across the corners is not a 4 sided polygon. Hence not a square.
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0i.e. the square is the quadrilateral that is both a rectangle and a rhombus. – 2012-07-28
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1I don't think that drawing a diagonal can _remove_ the innate squareness of the shape that was already on the paper before the diagonal was drawn. The square is still a square -- it is just not the only thing on the paper anymore. – 2012-07-28
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0I tend to agree with Henning and Andre but I asked the question because it arose in a square counting puzzle and now I wonder whether the definition is as William suggests. – 2012-07-28