To construct a #ParallelLine to a given line (in blue) in 2D #EuclideanSpace, all you need to do is pick two #points and draw #circles centred at those points of a specified #radius. Draw a #perpendicular to the line at each point (in red) and then draw a new line passing through the intersection of the perpendicular with the circles and there is the line parallel to the original one. Here is the process shown in #Geogebra.

#Mathematics #Geometry #EuclideanGeometry #FreeSoftware