Geometry Parallel: Relation used in geometry

Parallel lines or planes are next to each other, but never touch each other. This means they never intersect at any point. If two lines ${\displaystyle \ell _{1}}$ and ${\displaystyle \ell _{2}}$ are parallel, then we describe this by writing ${\displaystyle \ell _{1}\parallel \ell _{2}}$. The slopes of parallel lines are always equal.

Even if these two line segments were extended to infinity, there would never be a point of intersection between the two of them. In fact, two parallel lines in the two-dimensional plane are always a fixed distance apart.

• Non-Euclidean geometry
• Parallelogram
• Parallel postulate
• Perpendicular