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Khurram Wadee ✅

To construct a to a given line (in blue) in 2D , all you need to do is pick two and draw centred at those points of a specified . Draw a 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 .

You can also explore -Euclidean space and here is the same action in (here in a ). are replaced by which look like which intersect the at . Circles are transformed to circles but their hyperbolic centres are not at their Euclidean centres.

Repeating the construction for Euclidean space, you can see that the parallel lines diverge.