The Common Edge And Angle Theorem And Its Application In Teaching

In the preface to the 1978 National Mathematics Competition for Middle School Students,the famous mathematics master Luogeng Hua proposed an interesting mathematical geometry problem.The master spent a lot of time to prove the equation.However,Academician Jingzhong Zhang was able to make the proof process of this equation very simple.The reason is that there is a new powerful tool for mathematics,the common edge theorem.The same as the common edge theorem,the common angle theorem is also the same,and it also plays a key role in solving many mathematical geometric problems.The use of the two theorems undoubtedly adds new solutions to plane geometry.At the same time,these two theorems also reduce the tedious calculation of plane geometry and the construction of auxiliary lines.This opens up a new way for students to learn plane geometry.In this paper,the application of the co-edge co-angle theorem in plane geometry and its combination with other theorems are introduced,and the suitable and feasible teaching design in middle school teaching is proposed.In the first chapter,the research background,research purpose,research significance,research content and research method of the common angle theorem are briefly described.In the second chapter,the system introduces the specific content of the coplanar coangular theorem.Whenever it involves only intersecting,parallel,line segment ratios on the same line,and area ratio topics,such questions can be used.Coangular theorem.Analysis of plane geometry topics,especially in junior high school geometry and competition.Under the premise of the known coangular theorem,Meishi's theorem,triangular cutting line theorem,and Mercedes' theorem can be reasoned with each other.This chapter mainly shows the reasoning process.In the third chapter,we study the application of the coplanar coangular theorem in the special case.In the similar triangle,in the Meishi theorem,in the butterfly theorem.These theorems are closely related to the coplanar coangular theorem and have a great help to solving geometric problems.In the fourth chapter,according to Boliya's problem solving table,it is explained byteaching examples that the co-corner theorem is a graph and applied to teaching,and shows the teaching design: the new lesson of the co-side theorem,the practice lesson of the co-side co-corner theorem.