A classroom activity for high-school students, aiming at introducing space geometry from plane geometry has been introduced back in 2009 by Mammana, Margarone, Micale, Pennisi and Pluchino (2009a). The activity was based on the use of a Dynamic Geometry System and of the analogy between figures. Several aspects of the activity have been studied in different research studies. What we focus on, in this paper, is the power of the Dynamic Geometry System and of the analogy in the proof phase when working in a three dimensional environment, highlighting the cognitive process evolving in some 3D geometry proofs, by using videos recorded during the activities in the classroom.