 Manipulative 3: Rotational symmetry of a circle around the center of the circle. Created with GeoGebra. 

Symmetry of rotation refers to
geometric figures that, when rotated a certain angle about a center of rotation,
are coincidental with the original object. If two objects are coincidental, they are
identical in size, shape, and location. Manipulative 3 shows the symmetry
of rotation of a circle around the center of the circle. For any angle of rotation,
the rotated circle is
coincidental
with the original circle. The rotated circle always looks just like the original circle.

 Manipulative 4: Rotational symmetry of a square around the center of the square. Created with GeoGebra. 

In manipulative 4, the original square (in blue) and the rotated square are
coincidental only at three angles of rotation:
90° = π/2 rad,
180° = π rad, and
270° = 3π/2 rad.

 Manipulative 5: Rotational symmetry of a square around one of its corners. Created with GeoGebra. 

In manipulative 5, a square is rotated about one of its corners. Notice that the
original square and the rotated square are coincidental only with a full circle
rotation. So the square does not have rotational symmetry about one
of its corners.
