Kiepert triangles in an isotropic plane

In this lecture the concept of the Kiepert triangle of an allowable triangle in an isotropic plane will be studied. We are going to investigate the relationships between the areas and the Brocard angles of the standard triangle and its Kiepert triangle. It will also be proved that an allowable triangle and any of its Kiepert triangles are homologic. In the case of a standard triangle the expressions for the center and the axis of this homology will be given. A number of statements concerning the triangle and its Kiepert triangles are also going to be proved.