Question

Which of the following rotations turn a regular triangle onto itself? Pick ALL that apply (1 point)
П 45
Г 60
• 90
• 120
• 135
0 180
0 225
~ 240
• 270
• 315
П 360

Answer 1

To determine which rotations turn a regular triangle onto itself, we need to consider the symmetries of a regular triangle (equilateral triangle). The triangle can be rotated around its center, and certain angles will map the triangle onto itself.

A regular triangle has rotational symmetry at specific angles:

- 0° (360°)
- 120°
- 240°

This means that these angles will rotate the triangle and map it onto itself.

Now, checking the provided options:

- П 45 (45°) - does not map onto itself.
- Г 60 (60°) - does not map onto itself.
- • 90 (90°) - does not map onto itself.
- • 120 (120°) - maps onto itself.
- • 135 (135°) - does not map onto itself.
- 0 180 (180°) - does not map onto itself.
- 0 225 (225°) - does not map onto itself.
- ~ 240 (240°) - maps onto itself.
- • 270 (270°) - does not map onto itself.
- • 315 (315°) - does not map onto itself.
- П 360 (360°) - maps onto itself.

Thus, the rotations that turn a regular triangle onto itself are:

- 120°
- 240°
- 360°

Therefore, the correct answers are 120, 240, and 360.