Yes, if the perimeters are the same, then both of them have side = perimeter / 4. And of course the angles are all 90°, since they are squares.
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The word for the same in math is congruent. For example, if there are two squares, both the exact same size, length, width etc., then the two shapes are congruent.
I believe so, though I am not sure I can prove it.
No, because even through they have the same perimeter you must show how you can get 16 as the perimeter in two different ways.
same circle or congruent circles