“SAS”教案（名师）

1.3探索三角形全等的条件（边角边）教学设计

一、教学目标

在本课的教学中，不仅要让学生学会“边角边”这一全等三角形的识别方法，更主要地是要让学生掌握研究问题的方法，初步领悟分类讨论的数学思想.同时，还要让学生感受到数学来源于生活，又服务于生活的基本事实，从而激发学生学习数学的兴趣.为此，我确立如下教学目标：

知识目标：知道“边角边”这一三角形全等的识别方法. 能力目标：能利用“边角边”判别两个三角形全等，并解决一些简单的实际问题. 过程与方法：经历探索三角形全等条件的过程，体会分析问题的方法，积累数学活动的经验，

情感与态度：培养学生勇于探索、团结协作的精神. 二、剖析教材重难点

由于本节课是第一次探索三角形全等的条件，因此我确立了探究“边角边”这识别方法作为教学的重点，而将其发现过程以及边边角的辨析作为教学的难点.所以，我采用让学生动手操作、合作探究、媒体演示等多种方式来突破难点.

三、教学具准备

教具：相关多媒体课件；学具：剪刀、纸片、直尺.画有相关图片的作业纸. 四、教法选择与学法指导

根据本节课的特点，我将采用“研究性学习”的教学方法，在课堂教学让学生动手“做数学”，让学生进行合作学习，在“做”的过程中体会分类讨论的数学思想方法，遵循“教是为了不教”的原则，让学生自寻方法、自觅规律、自得知识、自悟原理. 五、教学流程

（一）创设情景，激发求知欲望

首先，我出示一个实际问题：

问题：某公司接到一批三角形架的加工任务，客户要求是所有的三角形必

须全等。客户为了使产品顺利过关，提出了明确的要求：要逐一检查三角形的三条边、三个角是不是都相等。部门职员小王提出了质疑：分别检查三条边、三个角这6个数据固然可以，但为了提高效率，是不是可以找到一个更好的方法，只量一个数据可以吗？两个呢？……

然后，教师提出问题：小王已提出了这么一个设想，同学们是否可以和小王一起来攻克这个难题呢？

设计意图：这样设计的目的是既交代了本节课要研究和学习的主要问题，将数学问题与实际生活相结合，又能较好地激发学生求知与探索的欲望.同时让学生知道数学知识无处不在，应用数学无时不有.符合“数学教学应从生活经验出发”的新课程标准要求. （二）引导活动，揭示知识产生过程

数学教学的本质就是数学活动的教学，为此，本节课我设计了如下的系列活动，旨在让学生通过动手操作、合作探究来揭示“边角边”判定三角形全等这一知识的产生过程. 活动一：1、让学生通过画图或者举例说明，只量一个数据，即一条边或一个角不能判断两个三角形全等.

2、让学生就测量两个数据展开讨论.先让学生分析有几种情况：即边边、边角、角角.再由各小组自行探索.同样可以让学生举反例说明，也可以通过画图说明. 3、在两个条件不能判定的基础上，只能再添加一个条件. 活动二：讨论第一种情况：各小组每人用一张长方形纸剪一个直角三角形（只用直尺和剪刀），怎样才能使各小组内部剪下的直角三角形都全等呢？主要是让学生体验研究问题通常可以先从特殊情况考虑，再延伸到一般情况. 活动三：出示课本上的3幅图，让学生通过观察、进行猜想，再测量或剪下来验证.并说说全等的图形之间有什么共同点.

A 1.5 45º

B 3 D 601.5 º

C E 3 M 3 F P 45º

N 1.5 M活动四：如图：(1)画∠MAN＝45º； (2)在AM、AN上分别截取AB=4cm,AC=5cm; (3)连结BC，剪下所的△ABC，与同学所剪的三

角形比较，它们全等吗？

BACN归纳总结：两边和它们的夹角对应相等的两个三角形全等．简写成“边角边”或“ＳＡＳ”

设计意图：在探索三角形全等的条件这一重要内容上，设计了一系列的如：剪纸、画图、制作、猜想等各种形式的数学活动，创设了贴近学生生活的、有趣的问题情境，目的在于让学生“做数学”的特色，让学生在做中感受和体验，在做中主动获取数学知识，感悟三角形全等的数学本质，归纳和明晰三角形全等的条件,紧扣《课标》中“注重经历观察、操作、推理、想象等探索过程”的要求.

（三）例题教学，发挥示范功能

例题教学是课堂教学的一个重要环节，因此，如何充分地发挥好例题的教学功能是十分重要的.为此，我将充分利用好这道例题，培养学生有条理的说理能力，同时，通过对例题的变式与引伸培养学生发散思维能力. 首先，我将出示课本例1，并设计下列系列问题，让学生一步一步地走向“知识获得与应用”的理想彼岸. 例题1：例1：如图，AB=AD，

∠BAC=∠DAC，请问：△ABC 和

△ADC是否全等？为什么？

ABCD

问题1：

请说说本例已知了哪些条件，还差一个什么条件，怎么办？（让学生学会找图形中的隐含条件）. 问题2：

你能用“因为……根据……所以……”的表达形式说说本题的说理过程吗？

问题3：

△ADC可以看成是由△ABC经过怎样的图形变换得到的？

在探索完上述3个问题的基础上，对例题作如下的变式与引伸：

△ABC与△ADC全等了，你又能得到哪些结论？连接BD交AC于O，你能说明△BOC与△DOC全等吗？若全等，你又能得到哪些结论？

设计意图：这样设计的目的在于体现“数学教学不仅仅是数学知识的教学，更重要的发展学生数学思维的教学”这一思想. 在例题教学的基础上，为了及时的反馈教学效果，也为提高学生知识应用的水平，达到及时巩固的目的，我设计了如下两个练习：

1、基础知识应用

如图，在△ABC和△DCB中，BC是公共边，如果∠ABC=∠DCB，只要再有 = ，也能说明△ABC≌△DCB

A

O

BDC2、讨论

：将“两边和它们的夹角对应相等”

改为“两边和其中一边的对角相等”这样的两个三角形还全等吗？

3、联系生活实际

春节期间,几名学生在钵池山公园，测量一池塘两端A、B间的距离，设计了如下方案：如图，先在平地上取了一个可直接到达A、B的点C，再连接AC，BC，并分别延长AC至D，BC至E，使DC＝AC，EC＝BC，最后测DE的长即为AB间的距离，你认为这种方案可行吗?并加以说明.

（四）课堂小结，建立知识体系. 1、经历了剪纸、测量、画图等方法探索三角形全等条件的活动过程、积累数学活动经验. 2、归纳得出了两个三角形全等的条件——SAS，知到了有两边和其中一边的对角对应相等的两个三角形不一定全等，初步发展了推理能力. 附板书设计:

探索三角形全等的条件

探究活动一:

两个三角形全等至少要几个条件

一个条件

行不通

两个条件

行不通

三个条件

探究活动二:

全等三角形的识别方法:

特殊------一般

观察------猜想------验证------结论------应用

识别方法一:两边和它们的夹角对应相等的两个三角形全等.简写成“边角边”或“SAS”

例题讲解：例题

练习巩固

ABCED

1.3

Explore the conditions for triangle complete equality instructional design I.

Teaching objectives In the teaching of this course, not only should the students learn the recognition method of "edge and corner", but also the students should master the method of studying problems and grasp the mathematics thought of classification discussion. At the same time, let students feel that mathematics comes from life, but also serve the basic fact of life, thus arousing studentsundefined interest in learning mathematics. To this end, I have established the following teaching objectives: Knowledge goal: know the full recognition method of the triangle "edge and edge". \Ability goal: can use "edge" to distinguish two triangles, and solve some simple practical problems. Process and method: to experience the process of exploring the complete conditions of triangles, to understand the methods of analyzing problems, and to accumulate experience in mathematical activities,

Emotion and attitude: cultivate studentsundefined spirit of exploration, unity and cooperation. II.

analyze the difficulty of teaching material Since this class is the first time to explore the condition of triangle holism, I have established the recognition method of exploring "edge and edge" as the key point of teaching, and regard the process of discovery and the discrimination of edge and corner as the difficulty of teaching. Therefore, I use students hands-on operation, cooperative exploration, media demonstrations and other ways to break through the difficulties. III.

Preparation of teaching aids Teaching aids: relevant multimedia courseware; learning tools: scissors, paper, ruler. Draw an assignment paper with related pictures. IV. Choice of Teaching Law and guidance of Learning Law According to the characteristics of this class, I will adopt the teaching method of "research-based learning", let the students start to "do mathematics" in the classroom teaching, let the students study in cooperation, and experience the mathematical thinking method of classification discussion in the process of "doing". Follow the principle

that "teaching is for the sake of not teaching". Let students find their own methods, laws, knowledge and principles. V. Teaching process (1)create situations to stimulate the desire for knowledge First of all, I show a practical problem: a company received a batch of triangulation processing tasks, customer request that all triangles must be equal. In order to make the product smooth clearance, put forward a clear request: to check the triangle of the three sides, the three angles are equal. Wang, a staff member of the department, questioned whether it was possible to examine the six data from three sides and three corners respectively, but in order to improve efficiency, could a better method be found, and only one data could be measured? Two?. Then, the teacher asked: Xiao Wang has put forward such an idea, students can work with Xiao Wang to overcome this difficult problem? Design intention: the purpose of this design is not only to explain the main problems to be studied and studied in this class, but also to combine mathematical problems with real life, and to stimulate the studentsundefined desire for knowledge and exploration. At the same time, let students know that mathematics knowledge is everywhere, applied mathematics is always there. According with the new

curriculum standard of "Mathematics teaching should start from life experience". (2)guiding activities to reveal the process of knowledge generation The essence of mathematics teaching is the teaching of mathematics activities. For this reason, I have designed the following series of activities in order to let students reveal the process of producing the knowledge of "edge, corner, edge" and so on by means of hands-on operation and cooperative inquiry. Activity 1: 1, let the student through drawing or illustrating, measure only one data, that is, one edge or one angle can not judge two triangles. 2. Let the students discuss the measurement of two data. First, let the student analyze several situations: edge, corner, corner. Then the teams will explore it themselves. Students can also give counterexample illustration, can also be illustrated by drawing. 3. Only one condition can be added on the basis of which two conditions cannot be determined. Activity 2: discuss the first scenario: each group uses a rectangular paper to cut a right triangle (only with a ruler and scissors). How can all the right triangles in each group be cut out equally?!? The main problem is to let students experience the research can be considered

from the special circumstances, and then extended to the general situation. Activity 3: show 3 pictures from the textbook. Ask students to observe, conjecture, measure or cut off to verify. And talk about what all the graphics have in common. A 1.5 45º

B 3 D 601.5 º

C E 3 F P M 3 45º

N 1.5

Activity 4: as shown in figure: (1) drawing MAN=45; (2) intercepting AB=4cm,AC=5cm; (3) linking BC, clipped ABC, on AM,AN and comparing them with triangles cut by students, are they all equal?

MBACNSumming up: two triangles equal to each other in their angles. Abbreviated as "edges" or "SAS" Design intention: in exploring the condition of triangles, a series of mathematical activities, such as paper-cut, drawing, making,

conjecturing and so on, have been designed to create interesting problem situations close to the life of students. The purpose is to make students "do mathematics" characteristic, let students feel and experience in doing, take the initiative to acquire mathematical knowledge in doing, understand the mathematical essence of triangles, sum up and clarify the conditions of triangulation, etc. Attach importance to the exploration process of observation, operation, reasoning, imagination and so on. (3)

example teaching, giving play to demonstration function Example teaching is an important link in classroom teaching, so how to give full play to the teaching function of examples is very important. For this reason, I will make full use of this example, cultivate the studentsundefined reasoning ability, at the same time, develop the studentsundefined divergent thinking ability through the variation and extension of the example. First of all, I will show the textbook example 1 and design the following series of questions to let students step by step towards the ideal of "knowledge acquisition and application".

Example 1: as shown in figure，AB=AD，

A∠BAC=∠DAC，is △ABC and △ADC all equal? Why?

1. Application of basic knowledge BCDIn △ABC and △DCB, BC is a common edge, and ∠ABC = ∠DCB is also shown if there is only a second = ，Can also explain△ABC≌△DCB.

2, discussion: "the two sides are equal to their angles." Are two triangles all equal if they are changed to "the diagonal equality of two sides and one side"? 3.

Connecting with the reality of life During the Spring Festival, several students measured the distance between the two ends of a pond in Bochi Mountain Park. This paper takes a point C on the flat ground that can reach Agna B directly, then connects AC,BC, and extends AC to DBC to E, so that the length of DE measured by DC=AC,EC=BC, is the distance between AB. Do you think this scheme is feasible? And explain it.

EABCD(4)

Summary of class and establishment of knowledge system. 1.

It has experienced the process of paper cut, measurement, drawing and so on, and accumulated the experience of mathematical activity.

2. The condition of homogenicity of two triangles is concluded that SAS, knows that two triangles with equal diagonal correspondence between two sides and one side are not necessarily homogeneous, and the reasoning ability is preliminarily developed.