The open mouth theorem, or the scissors lemma, for orthocentric tetrahedra
It is quite evident, and Euclid proved it in Proposition 24, Book I of his Elements, that if an angle of a triangle is increased without changing the length of its arms then the opposite side also increases. In this paper it is shown that an analogue is still true in orthocentric tetrahedra (those with concurrent altitudes) but it is no longer true for general tetrahedra.
scientific article; zbMATH DE number 6121642
scientific article