An 8-car Ferris wheel is shaped like a regular octagon. Does the Ferris wheel have rotational symmetry? Explain.
To determine whether the Ferris wheel has rotational symmetry, we need to understand what rotational symmetry is. An object has rotational symmetry if it can be rotated by a certain angle and still appears exactly the same as its initial position.
A regular octagon has rotational symmetry because it can be rotated by certain angles (in this case, multiples of 45 degrees) and still maintain the same appearance. In the case of an 8-car Ferris wheel shaped like a regular octagon, it means that if you rotate the wheel by 45 degrees, 90 degrees, 135 degrees, and so on, the pattern of the cars will remain the same.
To demonstrate this, imagine placing a dot at the center of the Ferris wheel to act as the axis of rotation. As you rotate the wheel by the specified angles, you'll notice that each car still aligns perfectly with its original position. This indicates rotational symmetry.
In summary, the 8-car Ferris wheel shaped like a regular octagon does have rotational symmetry because it can be rotated by specific angles while maintaining the same appearance.