  The notion of geometric construction is introduced. This notion allows to
compare incidence configurations in the algebraic and tropical plane. We
provide an algorithm such that, given a tropical instance of a geometric
construction, it computes sufficient conditions to have an algebraic
counterpart related by tropicalization. We also provide sufficient conditions
in a geometric construction to ensure that the algebraic counterpart always
exists. Geometric constructions are applied to transfer classical theorems to
the tropical framework, we provide a notion of incidence theorems and prove
several tropical versions of classical theorems like converse Pascal, Fano
plane or Cayley-Bacharach.
