||Elementary proof of Pavillet tetrahedron properties
||Axel PAVILLET and Vladimir SHELOMOVSKII
In this paper, we describe methods of elementary proof for the properties of the Pavillet tetrahedron. This solid gives students a great opportunity for in-depth study of perpendicularity in space and testing of various methods of proof. We have derived new methods for proving some theorems of plane triangle geometry, for example, the existence of the Gergonne point, the perpendicularity of Soddy line and Gergonne line.