Resumen: Pappus'' Involution Theorem is useful for proving incidence relations in the hyperbolic and elliptic planes. This fact is exemplified with the proof of a theorem about a family of 4-gons in the hyperbolic and elliptic planes. This non-Euclidean theorem is also re-interpreted in multiple ways, providing some other theorems for different figures in the hyperbolic plane. Idioma: Inglés Año: 2018 Publicado en: REVISTA DE LA UNION MATEMATICA ARGENTINA 59, 1 (2018), 143-156 ISSN: 0041-6932 Originalmente disponible en: Texto completo de la revista