A classroom report from a grade of T.C. deals with counter examples and suppossitions related to a tetraeder inscribed into a cube. In a first stage some distances, areas and volumes were calculated by help of analytic geometry; in addition some theorems ought to be proofed by means of the vector product. The problem came up to find all tetraeders of the same surface. In a second stage it was tried to solve this problem by a system of equations using DERIVE. It could be concluded hat the shapes of these tetraeder have to be acute angled, isometric triangles. In a third stage a purely geometrical approach resulted in the theorem: If the four shapes of a tetraeder have the same area, they are isometric in pairs. – Dans cet article l’auteur s’interroge sur la gestion au quotidien de contre-examples et de conjectures geometriques dans une classe de terminale scientifique. Il s’appuie sur une experience recue dans une classe de T.C. (ZDM/Mathdi)