For a student attending the initial years of the high school, it is not easy to fully realize what a geometrical object is. While speaking, for example, of a triangle, the teacher will underline that its sides have length, but no width and no thickness. However, a pupil has never seen an object of this kind in his daily experience. For, every straight line has a width and a thickness, however minimal they may be. How can we introduce the geometrical objects and, immediately afterwards, the geometrical reasonings so that the learners can accept them not based on a sort of faith act but relying on a real understanding? The best method is to explain their conceptual genesis, also adding some historical elements. Two abstract processes can be identified: the first one gave origin to the abstract objects, the second one to the propositions (axioms) on which the relations of such objects rely. Therefore, we suggest that the teacher dedicates two lessons to introducing the genetic bases of the geometrical thought before dealing with the mathematical details. In what follows, material for the two lessons is supplied.