The Parallel Tool

The parallel tool is used to calculate the parallel line to a given linear object (line, ray, or segment) through a point. In the figure below we select the segment (1) and the point (2) through which the parallel should pass. When we click the parallel tool the parallel to the segment through the point is constructed. Multiple parallels can be constructed in this way - just select the linear objects and points in successive pairs.
 
parallel example
 
In Hyperbolic Geometry, this tool has a very different effect, as there is no unique parallel to a given line through a point. Thus, when we click on the parallel tool we get two special parallels called ultraparallels. These are the unique parallels that intersect the linear object "at infinity", (in the case of the Poincare Model, they intersect on the unit circle).

hyper parallel

Finally, note that no parallels exist in Elliptic Geometry.