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[[File:Ultraparallel.png|thumb|200px|right|Poincaré disc model: The pink line is ultraparallel to the blue line and the green lines are limiting parallel to the blue line.]]
In [[hyperbolic geometry]], two lines
The '''ultraparallel theorem''' states that every pair of (distinct) ultraparallel lines has a unique common [[perpendicular]] (a hyperbolic line which is perpendicular to both lines).
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