巧用四点共圆解决中考压轴题

中考数学试题是以数学课程为标准,体现了初中学业水平的基础,也适度地体现了高一级学府的选拔功能。所 以,除了对基础知识的考查,也加大了对数学思想、逻辑能力、 应用能力的考查。尤其是中考试卷的后面二道压轴题,在培养 学生几何直观感觉,合理推理方向的作用体现更加突出。海珠 区2018学年期末考试第25题非常巧妙地融合了代数与几何的 综合内容,层层递进地巧妙设问。本文主要探讨第(3)问的解 法,本题第(3)考查了旋转图形这一基本模型和此类模型的基 本结论,并结合平面直角坐标系中点坐标公式和平面直角坐标 系两点间距离公式以及平面直角坐标系两直线垂直,斜率之积 等于负1,用三种方法解决此题。     

利用四点共圆 巧解中考试题

利用四点共圆可以快速解决有关问题,在解题教学中,教师要引导学生掌握四点共圆的条件和相关的几何图形,并利用圆的性质解决与角、线段的数量和位置关系有关的问题,进而发展他们利用四点共圆解决问题的意识和能力。     

平面几何中的四点共圆问题

四点共圆问题是国内外数学竞赛的一个重要内容.运用四点共圆知识往往可对某些竞赛问题给出极为简捷、新颖而又富于启发性的解答.四点共圆知识一般散见于初中平面几何教材.这里给出较为系统、明确的论述.1.若两直角三角形有公共斜边,则四顶点共圆.     

四点共圆问题

(本讲适合初中) “四点共圆”问题在数学竞赛中经常出现,这类问题一般有两种形式:一是以“四点共圆”作为证题的目的,二是以“四点共圆”作为解题的手段,为解决其他问题铺平道路。判定“四点共圆”的方法,用得最多的是统编教材《几何》二册所介绍的两种(即P89定理和P93例3),由这两种基本方法推导出来的其他判别方法也可相机采用。     

四点共圆问题

“四点共圆”是平面几何证题中一个十分有利的工具，四点共圆这类问题一般有两种形式：     

圆锥曲线中的一个四点共圆性质

正文[1]给出了直线与圆锥曲线位置关系的一个统一性质,笔者进一步探究,由文[1]中的性质推导得到了圆锥曲线中的一个四点共圆性质.文[1]中性质1已知椭圆Mx~2+Ny~2=1(M0,N0,M≠N)与直线l_1交于A、B两点,与直线l_2交于C、D两点,且A、B、C、D四点横坐标均不相同,若l_1与l_2的斜率互为相反数,则直线AC与直     

如何证四点共圆

四点共圆是《圆》一章的重要内容,在几何中应用较为广泛.如共圆呢?这里给同学们介绍五种方法.第一,利用圆的定义:即到一定点距离相等的各点共圆.例1如图1,试证明菱形ABCD各边中点E、F、G、H四圆.思路和证明:应用定义,去证OE=OF=OG=OH.这很容到,所以E、F、G、H共圆.第二,若两个(或多个)直角三角形共斜边,则各顶点.例2已知:如图2,AB和AC与⊙O相切于B、C,P是上一点,且PE⊥AB于E,PD⊥BC于D,PF⊥AC于F,求PD2=PE·PF.思路和证明:欲证PD2=PE·PF,即证PDPF=PEPD,只需证△PFDE.由于这里证边成比例比较困难,因而转证对应角…     

四点共圆的充要条件

定理1 设有二次曲线f_i:A_ix~2 B_ixy C_iy~2 D_ix E_iy F_i=0(i=1,2)。如果f_1与f_2有四个交点,则这四点共圆的充要条件是:     

四点共圆的应用

四点共圆的判定（如图,证明从略）：定理1对角互补的四边形内接于圆．即180°,则A、B、C、D共圆．定理2外角等于内对角的四边形内接于圆．即,则A、B、C、D共圆．定理3同底同侧张等角四点共圆．即,且都在△ABC和△ABD的公共边AB的同侧,则A、B、C、D共圆．定理4割线定理逆定理．即PA·PB=PD·PC,则A、B、C、D共圆．定理5相交弦定理逆定理．即MA·MC=MB·MD,则A、B、C、D共圆．四点共圆在几何证题中可以起到杠杆与桥梁的作用,它的应用可以扩展到各类题型．1．证两线段相等例1已知,在bABC中,／BAC一90”,AD上B…     

四点共圆的充要条件

本文给出两条二次曲线,两条直线与一条二次曲线,四条直线的四个交点共圆的充要条件。 定理1 设二次曲线 f_i:A_ix~2 B_ixy C_iy~2 D_ix E_iy F_i=0(i=1,2)。若f_1,f_2有四个交点,则这四点共圆的充要条件     

THE CRITICAL ROLE OF TWO-YEAR COLLEGES IN THE PREPARATION OF TEACHERS OF MATHEMATICS: SOME STRATEGIES THAT WORK

Providing high-quality mathematics instruction in the classrooms of the future is essential to the development of educated citizens and a competent workforce. W hile this need is growing, the United States is facing a critical teacher shortage. An estimated two million teachers are needed, and this situation will only worsen in the next decade. An increasing number of prospective teachers begin their college experience at two-year colleges, and many future elementary and middle school teachers take all of their college-level mathematics and science coursework at these institutions. Two-year colleges must be integrally involved in teacher recruitment and preparation. The National Science Foundation report Investing in Tomorrow's Teachers recommends two-year college involvement in teacher preparation, including recruitment of prospective teachers; strengthened undergraduate courses; preteaching experiences; liaisons between two-year colleges and four-year institutions; and connections with business, industry, and professional societies. The American Mathematical Association of Two-Year Colleges (AMATYC) has several strong teacher preparation activities and related guidelines. One successful model for two-year college involvement is the National Science Foundation-funded collaboration between Reynolds Community College and other two-year and four-year institutions in the area that has produced new and redesigned courses and a Teaching Apprentice Program. An emphasis on preparing prospective teachers to take licensure testing in mathematics is addressed through another program. A statewide initiative of the Virginia Community College System has produced a set of policy recommendations developed via a statewide task force and colloquium.     

大学物理题库建设中的几个问题之管见

本文结合作者在大学物理题库建设中的实践经验，就物理题库建设中的几个问题：题库结构、组卷方法、完善的题库的条件和要求、试题的难度和区分度、试卷的信度和效度等，谈了自己的认识。     

试论中学数学教师继续教育及其课程体系的设计

从分析一个优秀教学教师的现代标准同我国教师现状之间的差距，论述继续教育的必要性和课程设计的指导思想，并提出一份课程体系设计方案．     

我国四个区域房地产市场泡沫存在性检验

选取我国四大区域(东北区域、东部区域、中部区域、西部区域)2001年至2015年房屋销售价格指数和房屋租赁价格指数,首先对面板数据采用ADF单位根检验和Pedroni面板协整检验的方法来检验我国商品房房屋销售价格指数和房屋租赁价格指数的关系,然后分别对我国四大经济区域的房屋销售价格指数和房屋租赁价格指数的时间序列进行ADF检验和协整检验,最后得出我国东北、东部和中部区域房地产市场存在泡沫,西部区域房地产市场不存在泡沫的结论.     

北方游牧民族文化与中原汉文化的交汇融合

民族文化交融，是历史的必然，中华各民族的文化交融由来已久，当然，北方游牧民族与中原的文化交融亦在同步进行。而最广泛的交融体现在广大人民的生产劳动、衣食住行及巫术、宗教和民俗活动诸方面。     

CLASSROOM EXPERIENCES WITH NEW CURRICULUM MATERIALS DURING THE IMPLEMENTATION OF PERFORMANCE STANDARDS IN MATHEMATICS: A CASE STUDY OF TEACHERS COPING WITH CHANGE

A qualitative case study was conducted to investigate the classroom experiences of three sixth-grade teachers and their mathematics coach as they worked with new instructional materials during the implementation of a new state-mandated curriculum based on performance standards in mathematics. Teachers' collective participation in the exploration of the new standards, selection of materials, participation in a summer professional development workshop specifically tied to the use of the new materials, and the creation of an in-school professional development program were catalysts in the teachers' perception of the need to change their practice. The intended state-level standards were implemented with some success; however, despite their desire to change their practice and in contrast to their belief that considerable change had occurred, the data suggest that the change in the teachers' instructional practice was minimal.     

A CRITICAL APPRAISAL OF THE STATE OF EVALUATION IN HIGHER EDUCATION IN CANADA

This paper reviews some of the major recent developments in evaluation in Canadian universities and colleges, and identifies the factors which contribute to the success of these procedures. Programme evaluation, criteria of excellence, and evaluation of student learning are each considered in turn and the major issues discussed. The problems involved are clearly delineated and inevitably complex, particularly as they involve the twin questions of accountability and autonomy, but evaluation procedures are necessary in all three areas if rational decision‐making is to be typical of higher education.