Cauchy's Rigidity theorem says that if the corresponding faces of two convex polytopes are isometric (congruent) then the polytopes are related by a (proper or improper) motion.
Cauchy's biography (by Bruno Belhoste, Springer 1991) says that this statement is in Euclid book "9, Theorem 11". I checked: Proposition 11 in book 9 is not related to this. In general, book 9 is not about stereometry. English and French Wikipedia also say it is in Euclid, but do not say where exactly.
Can anyone tell where in Euclid can this (or similar, or related) statement be found?