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Math Help - Hyperbolic rigid motion

  1. #1
    Senior Member Pinkk's Avatar
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    Hyperbolic rigid motion

    Let AB and CD be geodesic segments of equal length. Prove that there is a hyperbolic rigid motion that maps A and AB onto C and CD, respectively.

    Once again, completely lost.
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    Senior Member Pinkk's Avatar
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    Any suggestions?
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  3. #3
    Senior Member Pinkk's Avatar
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    Okay, so I know the cases will probably have to divided up depending on if the geodesic segments are vertical lines or arcs of circles centered on the x-axis, and there has to be some inversion(s), but after that point I am just not sure.
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    so you're using the upper plane model of the hyperbolic geometry, are you?
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  5. #5
    Senior Member Pinkk's Avatar
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    Yes, the upper half plane, so the hyperbolic rigid motions we have covered so far are inversions where the center is located on the x-axis, horizontal translations, and reflections across vertical lines.
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