We can use the complementarity between Euclidean and Minkowskian geometries to find new constructions in the original Euclidean geometry in the following way:
1-Identify a property (or a theorem) in Euclidean geometry which involves the concept of perpendicularity.
2-Create a Geogebra (euclidean) construction to show this property
3-Make a GeoGebra applet using the same procedure as in 2 but using the corresponding spacetime tools.
4-Confirm the presence of a similar property
5- Transform this geometric property of spacetime into a euclidean property by substituting the st-counterparts by their euclidean names.
6-Substitute the reflections by the diagonal (which are the euclidean substitutes for the stPerpendiculars) by "directed reflections" (they invole the reflection by any direction, which must be fixed during all the construction steps but can be changed arbitrarily).
7-Indentify the regularities and geometric features of these constructions.
8- Try to find the locus of certain points when changing the direction arbitrarily. This can be assured previously by creating a circle centered at the origin and with a point on it (we will call it the "·direction slider"). Create a direction by joining the center of the circle with the direction slider. All directed reflections must be made about lines which are parallel to this "guided direction".
9-The results (if any) can be expressed geometrically to present a coherent property. It should be proved analyticallym however, before calling it a "theorem".
This is explored in a specific site: https://sites.google.com/site/euclideanproperties/