* As a dishclout to a kitchen: Petruchio says this when he refers to Katherina's role in the household. He is comparing her to a dishcloth, which is a lowly and insignificant object that is used for cleaning.
* As a dog to his master: Petruchio says this when he tells Katherina that she must obey him as a dog obeys its master. He is comparing her to a dog, which is a loyal and obedient animal.
* As a falcon to the lure: Petruchio says this when he compares Katherina to a falcon, which is a bird of prey that is trained to return to its owner's hand. He is saying that Katherina must be trained to return to him in the same way.
* As a cat will mew and stretch her neck: Petruchio says this when he describes the way Katherina will react when he scolds her. He is comparing her to a cat, which is a creature that is known for being irritable and easily offended.