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