Auxiliary Line Method From The Perspective Of Geometric Transformation

The plane geometry problem is difficult in how to make the auxiliary line.Therefore,people tried their best to create a variety of methods for the auxiliary line.But these methods were a brainstorm,without any practicality,in the face of a new plane geometry problem,in the end how to do the auxiliary line,people could not get inspiration from these existing methods.Later,people found that the geometric transformation can be used to solve the problem of the plane geometry effectively thus largely solve plane geometry as auxiliary line,but the geometric transformation belonged to solve a senior tool in plane geometry,the general high school students.So this paper puts forward far beyond reach in the discussion of auxiliary line method in plane geometry problem of geometric transformation based on perspective.Based on the background of geometric transformation,starting from the plane geometry problem conditions of the auxiliary line proposed translation assistant line and center reflective auxiliary lines,rotating auxiliary lines,axis reflective assistant line and auxiliary line,homothetic homothetic rotary assistant line and auxiliary line,homothetic axis reflection type inversion type auxiliary line eight types of practice,problems in plane geometry and in plane geometry in some of the classic historical title of domestic and international levels in the math contest as an example,introduces the eight methods of drawing auxiliary lines.At the same time,through more than and 10 different proofs of a plane geometry examples,the author illustrates the the powerful function of the eight auxiliary line method from the problem of the condition.