The collection of all points lying on one side of a line is called a half-plane.
Axiom
The line splits the plane into two half-planes.
The line a divides the plane into two half-planes.
The segments may lie in one half-plane or in different half-planes. So segments AB and CD lie in one half-plane, and segment EF in the other half-plane. It is easy to see that if a segment lies in one half-plane, then the ends of the segment lie in one half-plane and the segment does not intersect the straight, dividing plane into two half-planes.
If the ends of a segment lie in different half-planes, then the segment intersects the straight dividing plane into two half-planes. Point N lies in one half-plane, and point M lies in another half-plane. The segment MN intersects the line a.
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