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It is known that we can't with just a straight edge, given a line and a point out of the line in a plane to construct other line, passing through the point, parallel to the first. I know a proof of this fact lying on projective geometry.

However, I also know that is actually possible, with just a straight edge, given two parallel lines and a point out of both in a plane, construct a parallel to both lines and passing through the point. But I can't find neither the algorithm nor the demonstration of it.

Someone know how to do?

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  • $\begingroup$ With just a straight edge? Or are we allowed to use a compass as well? If you are allowed to use a compass, are you familiar with how to construct a right angle? $\endgroup$ – JMoravitz Jul 9 '15 at 2:57
  • $\begingroup$ Just a dry straight edge, nothing more. I barely remember the procediment... $\endgroup$ – João Dos Reis Jul 9 '15 at 3:04
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    $\begingroup$ Your title says to use a compass but your text says not. Which is it? $\endgroup$ – Rory Daulton Jul 9 '15 at 10:50
  • $\begingroup$ Wow, big mistake of mine. Without compass, I fixed the title. $\endgroup$ – João Dos Reis Jul 9 '15 at 14:16
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Idea: Constructuion is based on trapezoids

The idea

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