Parallel lines have so much in common. It's a shame they'll never meet.
Why this joke works
Together but Never Touching
Parallel lines share the same direction and remain the same distance apart, giving them plenty “in common.” In ordinary conversation, people with much in common seem destined to meet, but geometry prevents these lines from intersecting. Deliver the first sentence warmly, like the beginning of a friendship story. Let the second sentence sound genuinely regretful so the mathematical rule becomes the sad twist.
A closer look
Geometry Is Recast as a Missed Friendship
The first sentence applies relationship language to lines and sounds optimistic about their compatibility. “It’s a shame” then gives the narrator sincere sympathy before the geometric rule prevents an introduction. The plural subjects remain side by side throughout the thought, making their separation visible. That bittersweet delivery turns a static diagram into two characters whose defining similarity keeps them apart.
Fact behind the joke
Parallelism Extends Beyond Horizontal Lines
Parallel lines lie in the same plane, point in the same direction, and keep a constant separation rather than intersecting. Their orientation can be horizontal, vertical, or slanted; turning the whole diagram does not change the relationship. In three-dimensional space, lines can also fail to meet without being parallel if they are skew and do not share a plane.