Hjelmslev's Theorem
When all the points P on one line are related by an isometry to all points P^' on another, the midpoints of the segments PP^' are either distinct and collinear or coincident.
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Cite this as:
Weisstein, Eric W. "Hjelmslev's Theorem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/HjelmslevsTheorem.html