A very important tool in maths is to use symmetries to make problems easier. A symmetry of a shape is a movement that leaves it looking exactly the same. For example, rotating a square by \(90^\circ\) (spinning it by a quarter turn) is a symmetry. Imagine you are playing lights out on a board that has no quiet plans. Explain why if a light pattern has a certain symmetry, then its corresponding plan will also have the same symmetry.