'Pertain' is Latin for 'hold through to' — from 'per-' (through) + 'tenere' (to hold). Reaching relevance.
To be appropriate, related, or applicable to something; to belong as a part or feature.
From Old French 'partenir,' from Latin 'pertinēre' (to reach through, to extend to, to belong to, to relate to), a compound of 'per-' (through, thoroughly) + 'tenēre' (to hold). The Latin verb 'tenēre' is the direct descendant of PIE *ten- (to stretch, extend), one of the most productive roots in the Indo-European family. The same PIE root produced Greek 'teinein' (to stretch), Sanskrit 'tanoti' (he stretches), and the Latin cluster 'tenere / tendere / tensus' behind English
The word 'impertinent' originally meant 'not pertaining' — irrelevant, beside the point. It shifted from 'not relevant' to 'presumptuous' because making irrelevant remarks in serious company was considered rude. The logical step from 'beside the point' to 'insolent' happened over the fifteenth and