平行四边形性质在证明题中的应用

1、学习好资料欢迎下载平行四边形性质在证明题中的应用中英文翻译Parallelogram properties in the application of certificate in both English and Chinese translation平行四边形是为了后面学习矩形、菱形、正方形、圆，甚至高中立体几何打基础的，起着承 上启下的桥梁作用。Parallelogram is behi nd in order to study the recta ngle, rhombus, square, round, even high school lay the solid geometry,

2、 like play bridge.平行四边形本身的性质The n ature of the parallelogram itself平行四边形具有较多的性质，比如平行四边形对角相等以及对边相等等性质，另外，利用平行线的性质可以知道平行四边形的内错角相等，边延长线也可以引用平行线的性质得出同位角相等，这些性质在实际解题中均会经常用到，而且这些性质之间可以相互转化”首先，利用两个全等三角形拼成平行四边；然后，从这对全等三角形拼出的平行四边形，就可以得出平行四边形对边相等”、对角相等”的性质，特别是这一性质的证明更能体现这一数学思想，通过旋转和平移三角形，证明结论，作为教师在整个教学设计过程中需要

3、注重通过转化的思想方法，将平行四边形的问题转化为三角形的问题来解决，就能更好地解决教学内容的重点。Parallelogram has many properties, such as parallel quadrilateral diago nal are equal and the edge phase and so on properties, in addition, by using the properties of parallel lines can know parallelogram equals the alter nate An gle, the n ature of t

4、he edge parallel to the exte nsion cord can also refer to obtain corresponding Angle is equal, these properties often can be used in practical problem solvi ng, and can be "in to" each other betwee n these properties. First of all, the use of two congruent triangles into parallel edges; Th

5、en, from the parallelogram of congruent triangles to create, you can draw a parallelogram "of equal sides", the n ature of the "diago nal are equal", in particular the nature of the proof that can reflect the more mathematical thought, through the rotation and translation triangl

6、e, prove to the conclusion that as a teacher in the teaching needs to pay attention to in the design process through the way of thinking, the parallelogram into triangle problems to solve, can better solve the focus of the teach ing content. 添加辅助线将平行四边形化为三角形Adding auxiliary line will be a parallelog

7、ram into triangles添加辅助线将平行四边形化为三角形是初中阶段研究四边形问题的常用方法，它也是转化思想的重要体现。连接对角线，把平行四边形分割成两个全等的三角形，并利用全等三角形的性质得出平行四边形的性质，是研究平行四边形的一个重要方法，而学生对旋转、中心对称等知识了解不多，利用图形的变换来探究平行四边形可能会有一些困难，以前学生有了利用轴对称探索等腰三角形性质的经历和体会，教师只要适当地引领，学生的自主探索也就会水到渠成。另外，对于初中学生来说，通过度量，归纳出平行四边形的性质是没有难度的。Adding auxiliary line of the triangle is pa

8、rallelogram as junior high school stage study of quadrilateral com mon ly used method, it is also the tran sformatio n of the importa nt embodime nt of thought. Connected diagonal, cut the parallelogram into two congruent triangles, and by using the properties of con grue nt tria ngles con cludes th

9、at the n ature of the parallelogram, is an importa nt way to study a parallelogram, and stude nts don't know much about the kno wledge of rotati ng and center symmetry, using the graphic transform to explore parallelogram there may be some difficulties, students have before using the axisymmetri

10、c exploring the nature of the isosceles triangle experienee and experienee, the teacher as long as the lead appropriately, student's independent exploration and will follow. In addition, for junior high school students, through measureme nt, con cludes the n ature of the parallelogram is without

11、 difficulty.因此，在实际教学中应该让学生在通过操作、变换探究出平行四边形的性质的基础上，能发现的性质并进一步证明，这就要求他们能初步运用逻辑推理得出性质，而不是通过直观操作归纳得到平行四边形的性质，这时就让学生运用性质解决一些较简单的问题。In actual teaching, therefore, should let the student through the operation, on the basis of the transform to explore the nature of the parallelogram, can be found further ev

12、idenee, and the properties of preliminary by using logical reasoning that requires them to nature, rather than the nature of the parallelogram, are summarized through intuitive operation at this moment, let the student to utilize the properties of some relatively simple solution.不少学生经常不知道辅助线是怎么做的、为什

13、么这样做、有几种不同做法等问题。事实上如并体会对折”果学生在自主探究问题时，就要注重培养和锻炼他们探究问题的手段和方法,可以画中线、角的平分线、中位线等；平移”就可以画平行线，找同位角、内错角、同旁内角等；旋转”就可以画60° 90° 180°的角构造三角形等；以此引导学生添加适当的辅助线， 把未知化为已知，利用已学过的知识来解决新的问题，提高学生分析、解决问题的能力。当然，学生在学完了平行四边形性质后，就可以直接运用平行四边形性质解决的问题，不是再通过添加辅助线转化为平行线或三角形来解决，在构造全等三角形中兜圈子，而是运用新知识来解决问题，这就要培养学生熟练应用

14、此性质的习惯。Many students often don't know how to do auxiliary line is, why do this, there are several different practices and other issues. In fact if stude nts in in depe ndent inquiry, n eed to focus on training and exercise to explore the meansand methods of problem, they can draw experienee and

15、"folded" line, bisector of Angle, the median line, etc.; "Translation" can draw parallel lines, looking for corresponding Angle near, alternate Angle, with an internal Angle, etc.; "Rotation" can draw 60,90 , 180 Angle of triangle, etc.; To guide students to add the app

16、ropriate auxiliary line, turn the unknown into known as using have learned knowledge to solve new problems, improve the students' ability to analyze, solve the problem. Parallelogram properties after that, of course, students are learning, you can directly use parallelogram nature of the problem

17、, not by adding auxiliary line again into parallel lines or triangles, beat around the bush in the tectonic congruent trian gles, but use the new kno wledge to solve the problem, it will cultivate the habit of stude nts familiar with the n ature.三、平行四边形性质在证明题中的应用Three, the parallelogram n ature in t

18、he applicati on of the certificate平行四边形的诸多性质在初中几何证明题的解题过程中经常用到，例如证明线段相等，证明两角相等，证明线段的和差倍分，证明两直线垂直等解题中均常见。因此平行四边形在初中阶段的几何解题中起着非常重要的作用，对平行四边形性质的灵活应用也是初中几何教学的重点和难点。例如，证明两线段相等问题，已知： M是等腰三角开 ABC的底边上一点，过 M作ME/AC 交AB于E,作 MF/AB 交AC于F，试说明：BE=AF、CF=AE。这个题目 就要先说明四边形AEMF是平行四边形，再利用平行四边形对边相等的性质，并结合等腰三角形性质来进行解决。Parallelogram in junior high school geometry to prove the nature of the topic of the problem solvi ng process is often used, for example prove that li ne segme nts equal, prove two equal An gle, proof of line segme nt and the bad times, prove that the two straight line vertical are com mon in