Final answer:
The line that divides a circle into two equal halves is called the diameter. It passes through the circle's center, with its ends on the boundary of the circle. The concept is similar to a great circle on a sphere, like Earth's equator, which also divides it into two equal halves.
Step-by-step explanation:
The line that divides a circle into two equal halves is called the diameter. The diameter passes through the center of the circle and terminates at points on the circle's boundary. If you imagine holding a ruler at its midpoint, similar to an experiment where a ruler oscillates, and align it such that each end touches the edge of the circle, you have visually demonstrated the concept of a diameter cutting the circle in half.
Every circle also has a corresponding great circle when we consider the circle as being on the surface of a sphere, like on Earth. The Earth's equator is an example of a great circle that divides the sphere into two equal halves. Whether in two dimensions or on a spherical surface, the primary concept of bisecting a shape into two equal parts remains consistent through the use of a straight line known as the diameter or great circle.