# Parallel lines theorem

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• February 12th 2010, 04:43 PM
Pinkk
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.
• February 13th 2010, 10:43 AM
sfspitfire23
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