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 Web Resource. https://mathworld.wolfram.com/HjelmslevsTheorem.html