How do Sanskrit and Avestan words for Aryan show a common heritage?

The Sanskrit word ārya- and the Avestan word airiia- (along with the Old Persian ariya-) demonstrate a common heritage because they represent cognate terms used by speakers of both Indo-Iranian language subgroups to refer to themselves as a people.1

These linguistic correspondences, alongside shared religious terminology—such as the Sanskrit yajña- and Avestan yasna- (meaning "rite of worship" or "sacrifice")—provide clear evidence of the close historical and cultural relationship between the Indo-Aryan and Iranian groups. This shared nomenclature reflects their common origin as a distinct subgroup of the Indo-European language family.1