Given a parallelogram ABCD and a point E, construct F, symmetric to E w.r. to A, G symmetric to F w.r. to B etc. The resulting polygon EFGH closes i.e. the symmetric of H w.r. to D is again E.
This leads to a way to construct all quadrangles with given diameters in length and directions. Here the parallelogram (ABCD) and point E are movable (through the selection-tool (CTRL+1)).
The same subject, for general quadrangles, is handled in the file: SymmetriesOnVerticesEven.html .