A quarter of a circle has one rotational symmetry. Specifically, it can be rotated by 90 degrees to map onto itself. This means the only symmetry that corresponds to rotation is a 90-degree turn, as other rotations would not preserve the shape of the quarter circle. Thus, it has a single rotational symmetry.
An ellipse has rotational symmetry of order 2.
None, however the semicircle has one folding axis of symmetry perpendicular to the midpoint of the straight side
A seven-pointed star has seven rotational symmetries. This means it can be rotated in increments of ( \frac{360^\circ}{7} ) and still appear unchanged. Each of these rotations corresponds to one of the seven points of the star. Therefore, the total number of rotational symmetries is equal to the number of points.
An isosceles trapezoid has one rotational symmetry, which is a 180-degree rotation. This means that if you rotate the trapezoid by 180 degrees around its center, it will look the same as it did before the rotation. In addition to this, it has line symmetries, but regarding rotational symmetry specifically, there is only one.
A regular decagon, which has 10 equal sides and angles, has 10 rotational symmetries. These symmetries correspond to the decagon being rotated by multiples of (36^\circ) (360° divided by 10), including the identity rotation (0°). Therefore, the decagon can be rotated to match its original position in 10 different orientations.
It has 8 rotational symmetry.
Infinitely many.
An ellipse has rotational symmetry of order 2.
2
None, however the semicircle has one folding axis of symmetry perpendicular to the midpoint of the straight side
5
9 reflection
18
Two.
A regular hexagon has 6 rotational symmetries (rotational symmetry of order six) and 6 reflective symmetries (six lines of symmetry).
A seven-pointed star has seven rotational symmetries. This means it can be rotated in increments of ( \frac{360^\circ}{7} ) and still appear unchanged. Each of these rotations corresponds to one of the seven points of the star. Therefore, the total number of rotational symmetries is equal to the number of points.
A kite has only one line of rotational symmetry, as it is only the same if it is tilted once. (back to its normal position).