Several geometric books introduce the models of the hyperbolic plane, the connections and the isomorphisms between them. This short article presents the connections of the most familiar models of the hyperbolic plane in the same figure. These connections are based on proper projections. Let the Poincare model (G) be defined on the hemisphere x + y + z=1, z > 0. In this model the lines are the half-circle sections whose planes are perpendicular to the xy-plane. (Detailed description in [BJ].) Let the Weierstrass model (W) be on the sheet z > 0 of the hyperboloid x + y− z = 1 ([FR]). The lines of this model are the hyperbola-branch sections whose planes pass through the point O(0, 0, 0). Let the Klein-Poincare circle model (K) be defined on the circle domain x + y < 1 on the plane z = 0, in this model the lines are the diameters and the circular arcs intersecting the base circle perpendicularly. The Cayley–Klein model (C) is defined on the circle domain x + y < 1 on the plane z = 1, where the lines are the chords of the base circle ([BJ], [SZP]).