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Given 2 squares in the same plane join any corner of one square to a corner of the other square. Continue joining corners going in the same direction(clockwise or anticlockwise). Using only rotation, translation and symmetry concepts can you prove that the midpoints of the four segment lines connecting the 8 corners are vertices of a square?

Whats My Name
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    Questions usually have question marks somewhere around the end of them. What's your question here? – Asaf Karagila Feb 23 '13 at 14:18
  • What operations exactly do you allow? How would you prove that the result is a square using only those concepts? – vonbrand Feb 23 '13 at 14:24
  • For example : think about a rotation of the plane about a fixed point from which the conclusion will follow.(That is: if I take the midpoint of the line connecting the centers of the two squares and rotate the plane around this point 4 times with 90 deg. can I conclude that the figure is indeed also a square?) – Whats My Name Feb 23 '13 at 16:53

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