Synonyms for Impertinence (same or very similar meaning)
WordNet sense 1 (an impudent statement):
cheek, impudenceWordNet sense 2 (the trait of being rude and impertinent; inclined to take liberties):
cheekiness, crust, freshness, gall, insolenceWordNet sense 3 (inappropriate playfulness):
archness, perkiness, pertness, saucinessFrom the ODE community, based on WordNetadd/edit