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Math Help - Parallel lines theorem

  1. #1
    Senior Member Pinkk's Avatar
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    Parallel lines theorem

    Let m and n be two parallel straight lines. Let AB be a line segment that first intersects m and then n, that is perpendicular to both m and n, and whose length is twice the distance between m and n. Then, \rho_{n} \circ \rho_{m} = \tau_{AB}; the compositions of the two reflections is a translation.

    Once again, I'm clueless as to proving this.
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  2. #2
    Senior Member sfspitfire23's Avatar
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    Oct 2009
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    Well, thet composition of two indirect isometries is a direct isometry...
    A direct isometry can only be a rotation or translation....show the composition cannot be a rotation
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