等腰三角形

各位考官：

　　大家好，我是初中数学组的***号考生，我试讲的题目是《等腰三角形》，下面开始我的试讲。

　　一、问题导入

　　师：请同学们拿出一张长方形的纸片，并将纸片对折，然后剪去（或用刀子裁）一个角，再把它展开，大家观察一下，看得到的是一个什么样的三角形呢？

　　师：对，剪出来的图形是等腰三角形，今天我们一起学习等腰三角形的性质。

　　二、新课讲授

　　师：现在大家分组讨论一下，看看什么样的三角形称作等腰三角形呢？

　　师：生1说有两条边相等的三角形，叫做等腰三角形。

　　师：回答得非常正确。相等的两条边就叫做三角形的腰，另一边叫叫做三角形的底，两腰所夹的角叫做顶角。

　　师：那等腰三角形是轴对称图形吗？

　　师：请最后一排靠窗的男生回答一下。

　　师：这位同学说是，大家觉得呢？如果是，大家能找到对称轴吗？

　　师：等腰三角形是轴对称图形，但是它的对称轴不是其中线，因为中线是线段，而对称轴是直线，所以等腰三角形的对称轴是中线所在的直线。

　　师：下面我们再来看看等腰三角形的性质。先观察一下刚才折的图形。

　　师：△ADB与△ADC有什么关系？图中哪些线段或角相等？AD与BC垂直吗？

　　师：大家观察得很仔细。△ADB≌△ADC，∠B=∠C，∠BAD=∠CAD，∠ADB=∠CDA，BD=CD，这些结论都很正确。我们可以将这些结论转化为等腰三角形的性质。

　　师：性质1：等腰三角形的两个底角相等，简称：等边对等角。大家能不能将这个性质转化为数学语言呢？

　　师：生2的回答是：“已知在△ABC中，AB=AC，求证：∠B＝∠C”。

　　师：现在条件写出来了，大家试着证明一下。

　　师：同学们思路很清晰，先作△ABC的中线AD，则BD=CD。

　　师：大家课后可以思考一下，如果作底边的高或作顶角的角平分线能不能证明出来呢？

　　师：等腰三角形还有一个性质2：等腰三角形顶角的角平分线、底边上的中线、底边上的高三线重合。简称：三线合一。

　　师：下面大家试着证明一下，先写出已知和求证来。

　　师：大家写得都不错。

　　三、巩固练习

　　师：大家一起来看一道例题：如图在△ABC中，AB=AC，∠BAC=120°，点D，E是底边的两点，且BD=AD，CE=AE，求∠DAE的度数。

　　师：自己动手算一算，等下请一位同学说下他的答案。

　　师：生3说得完全正确，就是60°。运用的是等腰三角形的性质1，等边对等角。看来，大家掌握了等腰三角形的性质。

　　四、课堂小结

　　师：同学们，这节课你们有什么收获呢？大家发表一下自己的看法。五、作业布置

　　师：大家完成课后第1题，总结等腰三角形的性质并证明一下。

　　师：好，下课，同学们再见！

Dear examiners:

Hello everyone, I am the No. 1 candidate in the mathematics group of junior high school. The topic of my trial is "Isosceles Triangle". Now I will start my trial.

1. Problem introduction

Teacher: Ask the students to take out a rectangular piece of paper, fold it in half, then cut (or cut with a knife) a corner, and then unfold it. Observe what kind of triangle you can see. Woolen cloth?

Teacher: Yes, the figure cut out is an isosceles triangle. Today we will study the properties of an isosceles triangle together.

2. Lectures on new courses

Teacher: Now let’s discuss in groups, what kind of triangle is called an isosceles triangle?

Teacher: Sheng 1 said that a triangle with two equal sides is called an isosceles triangle.

Teacher: The answer is very correct. The two equal sides are called the waist of the triangle, the other side is called the base of the triangle, and the angle between the two waists is called the vertex angle.

Teacher: Is an isosceles triangle an axisymmetric figure?

Teacher: Please answer the boy in the last row by the window.

Teacher: This classmate said yes, what do you think? If yes, can you find the axis of symmetry?

Teacher: An isosceles triangle is an axisymmetric figure, but its axis of symmetry is not its midline, because the midline is a line segment and the axis of symmetry is a straight line, so the axis of symmetry of an isosceles triangle is the straight line where the midline is located.

Teacher: Now let's look at the properties of an isosceles triangle. Take a look at the graph you just folded.

Teacher: What is the relationship between △ADB and △ADC? Which line segments or angles are equal in the figure? Is AD perpendicular to BC?

Teacher: Everyone observes it very carefully. △ADB≌△ADC, ∠B=∠C, ∠BAD=∠CAD, ∠ADB=∠CDA, BD=CD, these conclusions are all correct. We can translate these conclusions into the properties of isosceles triangles.

Teacher: Property 1: The two base angles of an isosceles triangle are equal. Can you translate this property into mathematical language?

Teacher: Student 2's answer is: "It is known that in △ABC, AB=AC, and the proof is: ∠B=∠C".

Teacher: Now that the conditions are written down, everyone will try to prove it.

Teacher: The students have a very clear idea. First make AD of the center line of △ABC, then BD=CD.

Teacher: After class, you can think about it, if the height of the base side or the angle bisector of the top angle can be proved?

Teacher: The isosceles triangle also has another property 2: the angle bisector of the top angle of the isosceles triangle, the midline on the base, and the high three lines on the base coincide. Abbreviation: three lines in one.

Teacher: Now let's try to prove it, first write what we know and verify.

Teacher: Everyone's writing is good.

3. Consolidation exercises

Teacher: Let’s take a look at an example problem: As shown in the figure in △ABC, AB=AC, ∠BAC=120°, points D and E are the two points of the base, and BD=AD, CE=AE, find ∠DAE degree.

Teacher: Do the math by yourself, and ask a classmate to give his answer later.

Teacher: Sheng 3 is absolutely correct, it is 60°. Using the property 1 of an isosceles triangle, equilateral to equiangular. It seems that everyone has mastered the properties of an isosceles triangle.

4. Class Summary

Teacher: Students, what did you gain from this class? Please express your opinion. Five, work arrangement

Teacher: Everyone complete the first question after class, summarize the properties of an isosceles triangle and prove it.

Teacher: Okay, get out of class is over, goodbye students!