Puente Muñoz, María Jesús De LaAnsola Fernández-Enríquez, Maria Macarena2023-06-202023-06-202009-111439-851610.1007/s10114-009-7345-yhttps://hdl.handle.net/20.500.14352/41950We define transversal tropical triangles (affine and projective) and characterize them via six inequalities to be satisfied by the coordinates of the vertices. We prove that the vertices of a transversal tropical triangle are tropically independent and they tropically span a classical hexagon whose sides have slopes ∞, 0, 1. Using this classical hexagon, we determine a parameter space for transversal tropical triangles. The coordinates of the vertices of a transversal tropical triangle determine a tropically regular matrix. Triangulations of the tropical plane are obtained.engjournal articlehttp://0-www.springerlink.com.cisne.sim.ucm.es/content/104538/open access512.7Tropical trianglesTropical triangulationLinear inequalitiesConvexityTropical semi-fieldGeometria algebraica1201.01 Geometría Algebraica