## Problem of the Week

**Hjelmslev's Theorem**

-------10/1/07-------

Prove Hjelmslev's Theorem, which states that if the points *P* on a line are mapped by plane isometry onto the points *P'* of another line, then the midpoints of the segments *PP'* either coincide, or they are distinct and collinear.

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__Geometry: A Comprehensive Course__)