人们常说“音乐无国界,数学亦无国界”.虽然数学研究主要依靠学者个人的思考、钻研与攻关,但是相互间的交流、讨论与启发也起着重要作用.数学内部知识体系不更应该如此,相互盘根错节.普通高中课程标准实验教科书人教A版(以下简称教材)选修4-1《几何证明选讲》,教材要求学生理解相似三角形的定义与性质,了解平行切割定理,会证直角三角形的射影定理、圆周角定理、圆的切线判定定理与性质定理、相交弦定理、圆内接四边形的性质定理与判定定理、切割线定理等,会用 People often say that “there is no boundary between music and mathematics without boundaries.” Although mathematics research relies mainly on the individual’s thinking, research and research, scholars also play an important role in exchanging, discussing and enlightening each other. More should be so, mutual misgivings. Normal high school curriculum standard experimental textbook PEP A (hereinafter referred to as textbook) elective 4-1 “Geometry Proof”, the textbook requires students to understand the definition and nature of similar triangles, understand parallel cutting theorem, will Card Projection triangle theorem, circular angle theorem, the tangent of the circle to determine the theorem and the nature of the theorem, the intersection of chord theorem, circular quadrilateral nature of the theorem and decision theorem, cutting line theorem, will use