Draw a plane and a line through the center of a sphere. What if the plane or the line do not pass through the center of the sphere?
See solution.
Practice makes perfect
First, we will describe the number of types of planes that produce reflection symmetry in a hemisphere, that is in a half of a sphere. Then, we will describe the angles of rotation that produce rotation symmetry in the hemisphere.
Reflection Symmetry
First, let's analyze a hemisphere.
We are looking for a plane that produces reflection symmetry, so that it works like a mirror. Therefore, such a plane has to pass through the axis of symmetry of the hemisphere.
There are infinitely many planes that produce reflection symmetry in the hemisphere. Each such plan passes through the axis of symmetry of the hemisphere.
Rotation Symmetry
Just like before, let's first analyze a hemisphere and its axis of symmetry.
Note that the hemisphere can be mapped onto itself by a rotation of any angle about the axis of symmetry. Since there is only one axis of symmetry for the hemisphere, this is the only option.
