Another way to Construct a Parallel

The following method is somewhat easier if you wish to construct an accurate parallel to a line through a given point not on the line.  The idea is to make the opposite side of a rectangle with the given line on one side.

First construct a line perpendicular through the given point:

Then construct another perpendicular a convenient distance from this perpendicular:

 

Then set the compass to the distance from the line to P and mark off that distance on the newly constructed perpendicular:

Finally draw the parallel through P and the new point: 

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