Question
Which of the following rotations turn a regular triangle onto itself? Pick ALL that apply.
A. 45
B. 60
C. 90
D. 120
E. 135
F. 180
G. 225
H. 240
I. 270
J. 325
K. 360
A. 45
B. 60
C. 90
D. 120
E. 135
F. 180
G. 225
H. 240
I. 270
J. 325
K. 360
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To determine which rotations will turn a regular triangle onto itself, we need to consider the angle of rotation and the number of vertices (which is 3 for a triangle).
A regular triangle can be rotated by:
- 0 degrees (the identity rotation)
- 120 degrees (as it has symmetry for every vertex)
- 240 degrees (same reasoning as above)
Each of these rotations corresponds to rotating the triangle by multiples of its internal angle, which is \(360°/3 = 120°\).
Now let's evaluate the provided options:
A. 45 - **No**
B. 60 - **No**
C. 90 - **No**
D. 120 - **Yes**
E. 135 - **No**
F. 180 - **No**
G. 225 - **No**
H. 240 - **Yes**
I. 270 - **No**
J. 325 - **No**
K. 360 - **Yes**
The correct answers are **D (120), H (240), and K (360)**.
A regular triangle can be rotated by:
- 0 degrees (the identity rotation)
- 120 degrees (as it has symmetry for every vertex)
- 240 degrees (same reasoning as above)
Each of these rotations corresponds to rotating the triangle by multiples of its internal angle, which is \(360°/3 = 120°\).
Now let's evaluate the provided options:
A. 45 - **No**
B. 60 - **No**
C. 90 - **No**
D. 120 - **Yes**
E. 135 - **No**
F. 180 - **No**
G. 225 - **No**
H. 240 - **Yes**
I. 270 - **No**
J. 325 - **No**
K. 360 - **Yes**
The correct answers are **D (120), H (240), and K (360)**.
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