What is a characteristic behavior of parallel lines in a flat universe geometry?

They never meet

The behavior of parallel lines is a fundamental diagnostic for distinguishing between the three types of spatial curvature. In a flat universe, the geometry is Euclidean, meaning it follows the standard rules taught in high school geometry. In Euclidean space, two lines that start out parallel and proceed infinitely in the same direction will maintain a constant separation distance between them and will never intersect or meet. This contrasts with a closed universe (positive curvature) where parallel lines eventually converge, and an open universe (negative curvature) where parallel lines diverge and move farther apart over distance. This principle is essential because observations strongly suggest the universe is extremely close to being flat, implying that these Euclidean rules govern the cosmos on the largest observable scales.