Final answer:
An equilateral triangle has three rotational symmetries, which include 120-degree and 240-degree rotations, as well as the 360-degree rotation that returns the triangle to its original position.
Step-by-step explanation:
When considering the rotational symmetries of an equilateral triangle, we refer to the number of ways the triangle can be rotated around its center point and still look exactly the same as it did before the rotation. An equilateral triangle has three rotational symmetries: a 120-degree clockwise or counterclockwise rotation, a 240-degree rotation (which is equivalent to a 120-degree rotation in the opposite direction), and a 360-degree rotation, which brings the triangle back to its original position.
The symmetry after a 120-degree rotation occurs because when the triangle is turned one-third of a full circle, each vertex (corner) of the triangle has moved to the position of the next vertex, due to the triangle's sides and angles all being equal. Since the triangle returns to its initial orientation after a 360-degree rotation, this also counts as a position of symmetry, although it is the original position.