  In this article we exploit the fact that the special relativistic formula
which relates the energy and the 3-momentum of an elementary particle with its
rest mass, resembles the pythagorean theorem for right triangles. Using such
triangles, suitably arranged, we can prove all kind of equalities or
inequalities concerning the kinematical properties of elementary particles in a
wide variety of cases regarding particles' collision, decay or production.
Moreover, relations that are somehow hard to produce by the usual analytic
methods arise much more naturally through geometric constructions based on
right triangles.
