Question

1. which of the following is not an axiom about lines in the plane? (1) through two points only one straight line can be drawn. (2) through any point not on a given line, only one line can be drawn parallel to the given line. (3) a line segment connecting two points on the same side of a line must be parallel to the line. (4) two different lines will either intersect once or not at all.

Explanation:

Axioms about lines in a plane include that through two points, there is exactly one straight - line (1), and through a point not on a given line, exactly one line can be drawn parallel to the given line (2). Also, two different lines in a plane either intersect once or are parallel (4). A line segment connecting two points on the same side of a line is not an axiom about lines in a plane. It is just a description of a line - segment in relation to a line, not a fundamental truth about lines in a plane.

Answer:

(3) A line segment connecting two points on the same side of a line must be parallel to the line.