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"Prove: If two lines in the hyperbolic plane are asymptotic, then they do not admit a common perpendicular"

I'm trying to use something related to the angle of parallelism, but I guess it's not the right thing to do. Can someone suggest something? I feel kind of lost.

zoli
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Dalton
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1 Answers1

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If you can use the relationship of parallelism and the concepts of pole and polar then the following figure will help:

enter image description here

Here $a$ and $b$ are ultra parallel lines so the line joining their poles is their common parallel. It is clear that if $a$ and $b$ gets asymptotic then the latter line "goes out" of the hyperbolic plane

zoli
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