2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/139674The 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.46 Pages, 5 Figures V2. Major changes on the article, newer sections and results about geometric constructions and applications to prove theorems in tropical geometryAlgebraic Geometry16Y60; 51A30; 12K10; 14H50text