Final answer:
Rotations that will carry an equilateral triangle onto itself are those that are multiples of 120 degrees around the triangle's center, as this aligns with its threefold rotational symmetry. This includes 120 degrees counterclockwise and 240 degrees clockwise rotations.
Step-by-step explanation:
The rotations that will carry an equilateral triangle onto itself include any rotations by multiples of 120 degrees around the triangle's center because an equilateral triangle has threefold rotational symmetry. Rotations that result in the triangle coinciding with its original position are 120 degrees counter-clockwise, 240 degrees counter-clockwise (which is equivalent to 120 degrees clockwise), and a full rotation of 360 degrees (which can be considered as 0 degrees as well). So, the correct rotations that will carry this equilateral triangle onto itself from the given options are:
- 120° counterclockwise rotation about its center P
- 240° clockwise rotation about its center P
Other mentioned rotations such as 90°, 270°, 225°, or 200° will not align the triangle with its original position, as these are not divisors of the full 360 degrees that correspond to the triangle's symmetry.