Axiom of Parallels

The Axiom of Parallels is a fundamental rule in geometry that concerns lines and their angles. It states that through a point not on a given line, there is exactly one line parallel to the original line—meaning it never meets or crosses it. This axiom helps establish the consistent behavior of parallel lines, forming the basis of Euclidean geometry. In essence, it defines how parallel lines behave and ensures a predictable structure to the shapes and angles we study in this mathematical framework.