The hinge theorem holds in Euclidean spaces and more generally in simply connected non-positively curved space forms.
It can be also extended from plane Euclidean geometry to higher dimension Euclidean spaces (e.g., to tetrahedra and more generally to simplices), as has been done for orthocentric tetrahedra (i.e., tetrahedra in which altitudes are concurrent)[REF] and more generally for orthocentric simplices (i.e., simplices in which altitudes are concurrent) [REF].