Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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

share|cite|improve this question
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
Is a person wearing only a hat nude? Depends on what one is concentrating on. – André Nicolas Jul 28 '12 at 3:11

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.

share|cite|improve this answer
i.e. the square is the quadrilateral that is both a rectangle and a rhombus. – J. M. Jul 28 '12 at 2:29
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

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.