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Is a square with a diagonal drawn connecting two corners still considered a square? This is a question about the definition of a square.

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2  
I would say it's a dissected square... –  J. M. Jul 28 '12 at 2:11
    
Yes, 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? –  Will Jagy Jul 28 '12 at 2:26
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Is a person wearing only a hat nude? Depends on what one is concentrating on. –  André Nicolas Jul 28 '12 at 3:11

1 Answer 1

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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i.e. the square is the quadrilateral that is both a rectangle and a rhombus. –  J. M. Jul 28 '12 at 2:29
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I 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. –  Henning Makholm Jul 28 '12 at 3:31
    
I 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. –  daniel Jul 28 '12 at 14:47

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