Katherina and Bianca are like the north pole and south pole. They both have different characteristics and different natures.
KATHERINA:- Katherina is Baptista Minola's eldest daughter. She is an intolerable, curst, ill favored and shrewd young lady. She is famous in Padua for her scolding tongue. She is so "wild", unpleasant and hot tempered that no man wants to marry her. She thinks her father loves her sister Bianca more than he loves her. Katherina does not care about marriage and does not want any man to love her. She is disliked by everyone in the society (even by her own sister) because of her harsh and shrewish nature.
BIANCA:- Bianca is Baptista Minola's youngest daughter. She is a very beautiful, kind, "sweet" and unassuming young lady. She has a lot suitors (due to her look and her nature), but her father officially declares that he will not let anyone marry Bianca till he has found a husband for her shrewd sister Katherina. She is locked in a room, where she will learn Latin, music and poetry.