Parallel (geometry)

Parallel is a term in geometry and in everyday life that refers to a property of lines or planes. 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 ${\displaystyle \ell _{1}\parallel \ell _{2}}$.^[1][2] The slopes of parallel lines are always equal.

We can see that lines a and b are parallel because the angles between the lines and an intersecting line are the same.

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.^[3]

Construction

Related pages

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