Hjelmslev’s Theorem

https://upload.wikimedia.org/wikipedia/commons/thumb/5/51/Hjelmslev%27s_theorem.svg/640px-Hjelmslev%27s_theorem.svg.png

On each of these two black lines is a trio of red points marked by the same distances.

The midpoints of segments drawn between corresponding points are collinear.

(Discovered by Danish mathematician Johannes Hjelmslev.)