A very important tool in maths is to use symmetries to make problems easier. For today, define a symmetry of a shape as a movement that leaves the shape looking exactly the same as initial. 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.