Junior high school mathematics classroom teaching case one teaching goal
1, understand and master the judgment theorem and inference of isosceles triangle.
2. We can use its nature and judgment to prove that line segments or angles are equal.
Teaching emphasis: the judgment theorem of isosceles triangle and the application of inference
Teaching difficulties: correctly distinguish the judgment and nature of isosceles triangle, and prove the equality of line segments by using the judgment theorem of isosceles triangle.
Teaching process:
First, review the nature of isosceles triangle.
Second, the new grant:
I ask questions and create situations.
Play the slide show. In order to estimate the width of an east-west river, geologists choose a tree (point B) on the north bank of the river as the B mark, and then follow the southeast 60? When you walked a certain distance in the direction of C, did you measure it? ACB is 30 years old? At this time, geologists can know the width of the river by measuring the length of AC.
Students want to know, what is the basis for estimating river width in this way? With this question, guide students to learn? What is the judgment of isosceles triangle? .
II introduction of new curriculum
1. Judging from the proposition of the property theorem and the change of the conclusion, the content of the study is △ABC. B=？ C, so AB=AC?
What does it matter to make a triangle with two equal angles and then observe the two equal angles?
2. Guide students to write the known content and verify it according to the figure.
2. Summing up, through argumentation, this proposition is true, that is? What is the judgment theorem of isosceles triangle? The name of the blackboard theorem.
It is emphasized that this theorem is an important basis for transforming the equal relationship of the inner angles of a triangle into the equal relationship of the sides, which is similar to the property theorem. Equiangular equilateral? .
4. Guide students to tell the basis of geological expert investigation method in the cited examples.
Examples and exercises
1. as shown in figure 2.
Where △ABC is an isosceles triangle and []
2.① As shown in Figure 3, it is known that in △ABC, AB=AC. A=36？ And then what? C _ _ _ _ _ according to what? ).
(2) As shown in Figure 4, it is known in △ABC,? A=36？ ,? C=72？ , △ABC is a _ _ _ _ triangle (according to what? ).
What if it is known? A=36？ ,? C=72？ , BD split equally? When ABC crosses AC to D, it is determined that the isosceles triangle in Figure 5 has _ _ _ _ _.
(4) if known AD=4cm, BC _ _ _ _ _ cm.
3. Deduct L _ _ _ _ in the form of questions.
4. In the form of question 2 _ _ _ _ _, draw inferences from one another.
Example: If the bisector of the outer corner of a triangle is parallel to one side of the triangle, it is proved that the triangle is an isosceles triangle.
Analysis: instruct students to make pictures according to the meaning of the question, write what is known, verify and analyze the proof.
Exercise: 5. (l) As shown in Figure 6, in △ABC, AB=AC,? ABC？ The bisector of ACB intersects at point F, the crossing of F is DE//BC, it intersects with AB at point D, and it intersects with AC at point E. Which triangles in the diagram are isosceles triangles?
(2) In the above question, if the condition AB=AC is removed and other conditions remain unchanged, is there an isosceles triangle in Figure 6?
Exercise: P53 exercise 1, 2, 3.
IV class summary
1. How many methods are there to judge whether a triangle is an isosceles triangle?
2. How many methods are there to judge whether a triangle is an equilateral triangle?
3. What is the relationship between the property theorem of isosceles triangle and the judgment theorem?
4. Now it is proved that the problem of line segment equality should be considered from several aspects.
Homework: P56 Exercise 12.3 Questions 5 and 6
Case 2 teaching process of junior high school mathematics classroom teaching
I create situations and ask questions.
Review what we said last time about equilateral triangles.
1. An equilateral triangle is an axisymmetric figure with three axes of symmetry.
2. Every angle of an equilateral triangle is equal, equal to 60?
A triangle with three equal angles is an equilateral triangle.
4. Is there an angle of 60? An isosceles triangle is an equilateral triangle.
Where 1 and 2 are the properties of equilateral triangles; Method for judging equilateral triangles of 3 and 4.
Examples and exercises
1.△ABC is an equilateral triangle. Are the delta △ADE obtained by the following three methods all equilateral triangles? Why?
① Intercept AD=AE on AB side and AC side respectively.
2 work? ADE=60？ , d and e are on the AB side and AC side respectively.
③ Point D on intersection AB is DE∨BC, and intersection AC is at point E. 。
2. It is known that P and Q are two points on the side BC of △ABC, and PB=PQ=QC=AP=AQ. The size of BAC.
Analysis: It is known that the triangle APQ is an equilateral triangle, and each angle is 60? It is also known that △APB and △AQC are isosceles triangles with equal base angles, which can be deduced from the properties of the outer angles of triangles. PAB=30？ .
3.P56 exercise 1, 2
Three types of summary: 1. Isosceles and nature; Conditions of isosceles triangle
V assignment: 1 page. P58 exercise 12.3 question ll.
2. Given equilateral △ABC, find a point P on the plane so that any three of the four points A, B, C and P form an isosceles triangle. How many such points are there?
Junior high school mathematics classroom teaching case 3 teaching process
Firstly, review the judgment and properties of isosceles triangle.
Second, the new grant:
1. Properties of equilateral triangle: three sides are equal; All triangles are 60? ; The midline, height and angle bisector of the three sides are equal.
2. Determination of equilateral triangle:
A triangle with three equal angles is an equilateral triangle; There is a 60-degree angle? An isosceles triangle is an equilateral triangle;
In a right triangle, if an acute angle equals 30? Then the right-angled side it faces is equal to half of the hypotenuse.
Note: Inference 1 is an important method to judge whether a triangle is an equilateral triangle. Inference 2 shows that as long as one angle in an isosceles triangle is 600, it can be judged that the triangle is an equilateral triangle, regardless of whether the angle is the top angle or the bottom angle. Inference 3 reflects the relationship between the sides and angles of a right triangle.
3. Ask students to answer the example on page 148 of the textbook;
4. Supplement: As shown in the figure, in △ABC, BD is the center line on the AC side, DB? B. C.,
? ABC= 120o, verification: AB=2BC.
Analysis can be drawn from known conditions? ABD=30o, if we can construct a right triangle with an acute angle of 30o, the hypotenuse is AB, and the side opposite to the angle of 30o is a line segment equal to BC, the problem will be solved.
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