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