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Thread: Parallel lines theorem

  1. #1
    Senior Member Pinkk's Avatar
    Mar 2009
    Uptown Manhattan, NY, USA

    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, $\displaystyle \rho_{n} \circ \rho_{m} = \tau_{AB}$; 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
    Oct 2009
    Well, thet composition of two indirect isometries is a direct isometry...
    A direct isometry can only be a rotation or the composition cannot be a rotation
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