a hemisphere
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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.