To determine which of the given rotations turn a regular triangle (equilateral triangle) onto itself, we need to consider the property's symmetry of the triangle. A regular triangle has rotational symmetries corresponding to its three vertices.
The angles that will map the triangle onto itself are those that are multiples of \(120^\circ\) (since \(360^\circ / 3 = 120^\circ\)):
- \(0^\circ\) (identity rotation)
- \(120^\circ\) (one vertex goes to the position of the next)
- \(240^\circ\) (two vertices rotate to the position of the next)
This means the following rotations are valid:
- 120
- 240
- 360 (a full rotation, which is equivalent to \(0^\circ\))
Thus, the correct options are:
- 120
- 240
- 360
All other angles listed (45, 60, 90, 135, 180, 225, 270, 315) will not map the triangle onto itself.
1 answer