This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

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Here's the order of rotational symmetry for each shape:
i) Square A square can be rotated by , , and and still look the same as its original position. Including the rotation (which brings it back to the exact starting point), there are 4 such positions. The order of rotational symmetry for a square is .
ii) Equilateral triangle An equilateral triangle can be rotated by and and still look the same as its original position. Including the rotation, there are 3 such positions. The order of rotational symmetry for an equilateral triangle is .
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Here's the order of rotational symmetry for each shape: i) Square A square can be rotated by 90^, 180^, and 270^ and still look the same as its original position.
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.