The results reported in this article are based on PhD research conducted in a co-tutoring scheme between Italy and France in the domain of Euclidean geometry (Robotti, 2002). The article explores the processes involved in a problem of demonstration in plane geometry in a traditional school situation. Indeed, pupils, especially in grades 9 and 10 (the level we studied), are often confronted with this kind of problem. The idea was to analyze the solution of a problem of demonstration in plane geometry from a relatively new point of view in mathematics education, that is, to analyze the role of the natural language, especially pupils’ verbalizations, that is produced during the solution process. Indeed, natural language is a fundamental component of the demonstration process, which is why we wanted to see whether it could help the development of that process and, if so, how. Finally, we focused on the process of demonstration in plane geometry as a key element in mathematics teaching. Although mathematics education research has extensively addressed this element, open questions remain that have not been studied. Moreover, we chose to analyze the process of demonstration in Euclidean geometry because in Italy, as in France, it is a tradition to introduce students to demonstration in that domain. addressed these aspects, there are still open questions which have not been studied. In addition, we analyze the demonstration process in the Euclidean geometry domain given that it is also a tradition in France and Italy to introduce students to this domain.