Back in Padua, Tranio (as Lucentio) and the Pedant (as Lucentio's father Vincentio) wait for Baptista outside his house.
The Pedant is introduced to Baptista as Vincentio and the two men seem pleased with one another and the kids' engagement. They all agree to go to Lucentio's place to settle their business and sign some contracts.
Baptista sends "Cambio" (really Lucentio) to fetch Bianca and tell her the good news about her upcoming marriage to Lucentio.
Instead of fetching Bianca and taking her to her dad, Lucentio has caught up with Biondello, who brings him up to speed on the arrangements for his elopement with Bianca.
While Baptista is kept busy signing fake contracts with Tranio (as Lucentio) and the Pedant (as Vincentio), Bianca and Lucentio will go to St. Luke's church, where a priest is waiting.
Biondello tells Lucentio to get to the church ASAP and to make sure he has some reliable witnesses to confirm the marriage. Lucentio runs off to find Bianca.