Question
Which of the following rotations turn a regular triangle onto itself? Pick ALL that apply(1 point)
Responses
45
45
60
60
90
90
120
120
135
135
180
180
225
225
240
240
270
270
315
315
360
360
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Responses
45
45
60
60
90
90
120
120
135
135
180
180
225
225
240
240
270
270
315
315
360
360
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Answers
GPT-4o mini
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.
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.