What is the key characteristic of parallel lines in geometry?

The key characteristic of parallel lines in geometry is that they are two lines that never intersect, regardless of how far they are extended in either direction. This means that no matter the distance, the lines maintain a constant distance apart, which ensures that they will never cross each other.

This definition is fundamental in geometry and is a crucial aspect that distinguishes parallel lines from other types of lines. Understanding this characteristic helps to visualize and work with parallel lines in various geometric contexts, such as in the creation of shapes, angles, and in coordinate geometry.

The other choices do not accurately describe parallel lines - for instance, lines that intersect at one point or meet at infinity do not maintain the defining feature of parallelism, which is the absence of intersection at all points. Furthermore, the notion of convergence implies that the lines would eventually meet at some point, which is contrary to the definition of parallel lines.