Question

Which of the following rotations turn a regular triangle onto itself? Pick ALL that apply

45
60
90
120
135
180
225
240
270
315
360

Answer 1

To determine which rotations turn a regular triangle onto itself, we need to consider the symmetries of an equilateral triangle. A regular triangle (equilateral triangle) has rotational symmetries that occur at specific angles.

The angles that allow a regular triangle to map onto itself are multiples of \( \frac{360}{3} = 120 \) degrees, which corresponds to the three vertices of the triangle.

The relevant rotations that turn the triangle onto itself are:
- \( 0^\circ \) (or \( 360^\circ \))
- \( 120^\circ \)
- \( 240^\circ \)

Now let's check the given options:

1. 45 – **No**
2. 60 – **No**
3. 90 – **No**
4. 120 – **Yes**
5. 135 – **No**
6. 180 – **No**
7. 225 – **No**
8. 240 – **Yes**
9. 270 – **No**
10. 315 – **No**
11. 360 – **Yes** (as it is equivalent to a full rotation)

Thus, the rotations that turn a regular triangle onto itself are:
- 120
- 240
- 360

So the correct answers are **120, 240,** and **360**.