The modern approach to geometry places emphasis on symmetry and transformations of the Euclidean plane. Traditional geometry consists of a few basic axioms and a series of theorems, each of which is proved by reference to those earlier in the series. In this chapter a formal statement is made of some important theorems, with examples to show how they are applied to problems in geometry. In solving such geometrical problems any appropriate method, either modern or traditional, may be used and trigonometry is sometimes necessary.