Analysis And Exploration Of The Quadrilateral Problem Of Plane Geometry In Mathematical Competition

As one of the major academic competitions,the mathematics competition enjoys a good reputation in China.Plane geometry as the focus of the mathematics competition,and there are many studies on it.However,quadrilateral as one of the important components of planar geometry,the existing research is scattered and fragmented.Therefore,in order to perfect the quadrilateral system,the author takes the quadrilateral problem of plan geometry in mathematics competition as the research topic.Based on this,this paper adopts the literature analysis method and the statistical analysis method,taking the quadrilateral test questions of plane geometry in some mathematics competition as the research object,combining the research results of the predecessors on the quadrilateral,and analyzing the external structure and intrinsic characteristics of the examination questions.First of all,starting from the external structure of the examination questions,according to the statistics of the number of sessions of quadrilateral examination questions in each competition,the setting background of the questions and the types of questions,it is concluded that the proportion of sessions of quadrilateral examination questions in each competition is less than 40%.According to the collected examination questions,the examination questions with convex quadrilateral and cyclic quadrialaterl as the setting background were the most,which account for about 69%;Furthermore,prove the equation relationship of the line segment and four-point in concyclic are the most commonly tested types of measurement relation and position relation respectively,accounting for 46% and 42% of the two main types of questions.Then from the analysis of the inherent characteristics of the examination questions,combined with the previous research on the principle and method of the examination questions of competition,the paper extracted three proposition methods of the quadrilateral examination questions,which are "the citation of the quadrilateral theorem","the quadrilateralization of the triangle problem" and "the basic geometric structure".Among then,The "basic geometric structure" method is a proposition method from graph to question,which includes three structures: "four-point in concyclic","complete quadrilateral" and "harmonic".Finally,according to the proposed proposition method,using the geometric sketchpad as the medium,and taking a question has many variations and a question has many questions as the main line,the paper explores and proves some quadrilateral questions.In addition,a triangle examination question was developed independently and adapted to a quadrilateral examination question,with the help of the test question,Thirteen interesting conclusions were extended and corresponding proofs were given.