Which of the following figures in a plane separates it into half-planes?
F. A line
G. A ray
H. An angle
J. A point
K. A line segment
Answer (3)
F. A line ;
The figure in a plane that separates it into half-planes is a line. According to Theorem 5, every straight line (a) in a plane (a) divides the points of the plane into two separate regions with specific properties. If a point A is in one region and a point B is in the other, then any segment AB will intersect the line. Points A and A' within the same region can be joined without intersecting the line. Thus, the correct answer to the question is F. A line.
The figure in a plane that separates it into half-planes is a line (option F). A line divides the plane into two distinct regions known as half-planes. Other figures like rays, angles, points, or line segments do not achieve this separation.
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