“Good morrow, Kate, for that’s your name, I hear” (2.1.182).

This line occurs when Petruchio is introduced to Katherine for the first time. Petruchio has already revealed that he intends to combat Katherine’s tempestuous nature and secure her for his wife. He launches a series of manipulations throughout 2.1 and he begins by calling Katherine “Kate”. This is important for Petruchio’s characterization because it reveals his calculating and manipulative nature. His use of the nickname “Kate” cleverly disorients Katherine because it establishes a sense of false intimacy from the moment they meet. Petruchio exclusively refers to Katherine as “Kate” for the rest of the scene.  

“’Tis bargained ’twixt us twain, being alone, That she shall still be curst in company” (2.1.302-303).

Here, Petruchio tells the other men, including Katherine’s own father, that Katherine’s combative and fiery nature is actually just an act that the two of them have agreed upon together, thus revealing that Petruchio is a skilled orator and a masterful manipulator. He creates a plausible explanation as to why Katherine continues to rage against Petruchio even after they are engaged, undermining Katherine by claiming that her true self is simply an act, one that he is in on.

“My falcon now is sharp and passing empty,
    And, till she stoop, she must not be full-gorged,
    For then she never looks upon her lure.
    Another way I have to man my haggard,
    To make her come and know her keeper’s call” (4.1.171-175). 

In this famous speech, Petruchio compares Katherine to a wild falcon that must be weakened so that it can be domesticated. It is here that Petruchio reveals his plan to starve Katherine and never let her sleep so that she will become too weak to challenge him. The speech ends with Petruchio’s confident assertion that this is the only way to “tame a shrew,” which is where the play gets its title (4.1.191).