Baptista stops Katherine from abusing Bianca and receives a visit from Petruchio, who presents Hortensio (disguised as Litio, a music teacher); Gremio introduces Lucentio (disguised as Cambio, a teacher of languages). Tranio, impersonating Lucentio, announces his wish to marry Bianca, and Petruchio his desire to marry Katherine. Baptista insists that Petruchio must get Katherine’s love. Petruchio and Katherine, left alone, enter into a furious bout of wordplay. Petruchio then lies to Baptista, insisting that Katherine loves him but that the couple have agreed that she will pretend to dislike him in public. Katherine’s wedding is arranged, and Baptista hears the offers that Gremio and Tranio (as Lucentio) make for Bianca. Tranio-Lucentio outbids Gremio and is awarded Bianca, provided that Vincentio, Lucentio’s father, will guarantee the dowry. Tranio-Lucentio sets out to find someone to impersonate Vincentio and provide the guarantee.