Consider a rectangle. What happens when we rotate it 180^(∘) once? What about when we do it again?
Once
Practice makes perfect
We want to know how many times a figure that only has point symmetry can be rotated before it is back where it started. Let's consider a figure that has point symmetry. In other words, our figure should have 180^(∘) rotational symmetry, which means that a rotation of 180^(∘) maps the figure onto itself. An example of this type of figure is a rectangle.
As we know, rotating the rectangle once by 180^(∘) will map it onto itself.
Note, however, that the figure is not back where it started. The side that was on the top of the rectangle before the rotation is now on the bottom of the rectangle. Let's rotate the rectangle by 180^(∘) once more.
After rotating the figure by 180^(∘) for the second time, it is back where it started. Therefore, we can rotate the figure once before it is back to where it started.
