To define parallel lines, we primarily rely on two undefined terms from geometry: line and point.
A line is a straight path that extends indefinitely in both directions and has no thickness. It is one of the fundamental concepts in geometry, but it is not formally defined within the framework of geometric axioms.
A point represents a specific location in space, with no dimensions—just a position. Additionally, the concept of distance between points and the idea of angles between lines are also crucial as they help us understand the positioning of lines relative to one another.
Given these undefined terms, we can describe parallel lines as follows: Parallel lines are two lines that, when extended indefinitely, never intersect. This definition relies on understanding how lines are positioned in relation to one another, which is fundamentally linked to the concepts of points and lines themselves.