平行四邊形性質(zhì)在證明題中的應(yīng)用

1、學(xué)習(xí)好資料歡迎下載平行四邊形性質(zhì)在證明題中的應(yīng)用中英文翻譯Parallelogram properties in the application of certificate in both English and Chinese translation平行四邊形是為了后面學(xué)習(xí)矩形、菱形、正方形、圓，甚至高中立體幾何打基礎(chǔ)的，起著承 上啟下的橋梁作用。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.平行四邊形本身的性質(zhì)The n ature of the parallelogram itself平行四邊形具有較多的性質(zhì)，比如平行四邊形對(duì)角相等以及對(duì)邊相等等性質(zhì)，另外，利用平行線的性質(zhì)可以知道平行四邊形的內(nèi)錯(cuò)角相等，邊延長(zhǎng)線也可以引用平行線的性質(zhì)得出同位角相等，這些性質(zhì)在實(shí)際解題中均會(huì)經(jīng)常用到，而且這些性質(zhì)之間可以相互轉(zhuǎn)化”首先，利用兩個(gè)全等三角形拼成平行四邊；然后，從這對(duì)全等三角形拼出的平行四邊形，就可以得出平行四邊形對(duì)邊相等”、對(duì)角相等”的性質(zhì)，特別是這一性質(zhì)的證明更能體現(xiàn)這一數(shù)學(xué)思想，通過(guò)旋轉(zhuǎn)和平移三角形，證明結(jié)論，作為教師在整個(gè)教學(xué)設(shè)計(jì)過(guò)程中需要

3、注重通過(guò)轉(zhuǎn)化的思想方法，將平行四邊形的問(wèn)題轉(zhuǎn)化為三角形的問(wèn)題來(lái)解決，就能更好地解決教學(xué)內(nèi)容的重點(diǎn)。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. 添加輔助線將平行四邊形化為三角形Adding auxiliary line will be a parallelog

7、ram into triangles添加輔助線將平行四邊形化為三角形是初中階段研究四邊形問(wèn)題的常用方法，它也是轉(zhuǎn)化思想的重要體現(xiàn)。連接對(duì)角線，把平行四邊形分割成兩個(gè)全等的三角形，并利用全等三角形的性質(zhì)得出平行四邊形的性質(zhì)，是研究平行四邊形的一個(gè)重要方法，而學(xué)生對(duì)旋轉(zhuǎn)、中心對(duì)稱等知識(shí)了解不多，利用圖形的變換來(lái)探究平行四邊形可能會(huì)有一些困難，以前學(xué)生有了利用軸對(duì)稱探索等腰三角形性質(zhì)的經(jīng)歷和體會(huì)，教師只要適當(dāng)?shù)匾I(lǐng)，學(xué)生的自主探索也就會(huì)水到渠成。另外，對(duì)于初中學(xué)生來(lái)說(shuō)，通過(guò)度量，歸納出平行四邊形的性質(zhì)是沒(méi)有難度的。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，在實(shí)際教學(xué)中應(yīng)該讓學(xué)生在通過(guò)操作、變換探究出平行四邊形的性質(zhì)的基礎(chǔ)上，能發(fā)現(xiàn)的性質(zhì)并進(jìn)一步證明，這就要求他們能初步運(yùn)用邏輯推理得出性質(zhì)，而不是通過(guò)直觀操作歸納得到平行四邊形的性質(zhì)，這時(shí)就讓學(xué)生運(yùn)用性質(zhì)解決一些較簡(jiǎn)單的問(wèn)題。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.不少學(xué)生經(jīng)常不知道輔助線是怎么做的、為什

13、么這樣做、有幾種不同做法等問(wèn)題。事實(shí)上如并體會(huì)對(duì)折”果學(xué)生在自主探究問(wèn)題時(shí)，就要注重培養(yǎng)和鍛煉他們探究問(wèn)題的手段和方法,可以畫(huà)中線、角的平分線、中位線等；平移”就可以畫(huà)平行線，找同位角、內(nèi)錯(cuò)角、同旁內(nèi)角等；旋轉(zhuǎn)”就可以畫(huà)60° 90° 180°的角構(gòu)造三角形等；以此引導(dǎo)學(xué)生添加適當(dāng)?shù)妮o助線， 把未知化為已知，利用已學(xué)過(guò)的知識(shí)來(lái)解決新的問(wèn)題，提高學(xué)生分析、解決問(wèn)題的能力。當(dāng)然，學(xué)生在學(xué)完了平行四邊形性質(zhì)后，就可以直接運(yùn)用平行四邊形性質(zhì)解決的問(wèn)題，不是再通過(guò)添加輔助線轉(zhuǎn)化為平行線或三角形來(lái)解決，在構(gòu)造全等三角形中兜圈子，而是運(yùn)用新知識(shí)來(lái)解決問(wèn)題，這就要培養(yǎng)學(xué)生熟練應(yīng)用

14、此性質(zhì)的習(xí)慣。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、平行四邊形性質(zhì)在證明題中的應(yīng)用Three, the parallelogram n ature in t

18、he applicati on of the certificate平行四邊形的諸多性質(zhì)在初中幾何證明題的解題過(guò)程中經(jīng)常用到，例如證明線段相等，證明兩角相等，證明線段的和差倍分，證明兩直線垂直等解題中均常見(jiàn)。因此平行四邊形在初中階段的幾何解題中起著非常重要的作用，對(duì)平行四邊形性質(zhì)的靈活應(yīng)用也是初中幾何教學(xué)的重點(diǎn)和難點(diǎn)。例如，證明兩線段相等問(wèn)題，已知： M是等腰三角開(kāi) ABC的底邊上一點(diǎn)，過(guò) M作ME/AC 交AB于E,作 MF/AB 交AC于F，試說(shuō)明：BE=AF、CF=AE。這個(gè)題目 就要先說(shuō)明四邊形AEMF是平行四邊形，再利用平行四邊形對(duì)邊相等的性質(zhì)，并結(jié)合等腰三角形性質(zhì)來(lái)進(jìn)行解決。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