a hemisphere
The 2 halves in a circle are the 2 semi circles.
a line
They occur when you divide something on a line of symmetry.
A half of a quarter of a circle is 1/8 of a circle. There are four pieces making 1/4. If you split all of them into halves you have eighths.
I'm assuming you mean "What does dividing into two congruent parts mean?". It means to divide into two identical halves.
Hemispheres
Half a sphere is a hemisphere
When a circle is folded along its diameter, it creates two congruent halves or semicircles.
A line of symmetry divides a figure into two matching halves.
A great circle
This is called the longitudinal fissure. The halves are not actually separate.
Mountains
The 2 halves in a circle are the 2 semi circles.
The diameter of a circle divides it into two halves
That line is called a "Diameter".
a line
There is one line, the equator, that separates the northern from the southern hemisphere. The Greenwich Meridian and International dateline form a circle that separates the western from the eastern hemisphere. These are the standard hemisphere divisions of the globe, but every meridian circle divides the globe into 2 halves.