Judgement Theorem of Rectangle 1 2

Teaching purpose:

1, understand and master the judgment theorem of rectangle 1, 2; These theorems will be used for relevant argumentation and calculation;

2. Cultivate students' abilities of observation, practice, self-study, calculation and logical thinking;

3. The dialectical materialism view that things are always interrelated and different is permeated in teaching.

Teaching Emphasis: Judgment Theorem of Rectangle 1 2

Difficulties in Teaching: Proof Method and Application of Theorem

teaching program

First of all, review and introduce the creative feelings.

We already know the properties of rectangles:

Among them, the judgment methods of rectangle are: (definition) (two conditions)

The property is: Theorem 1, four corners of a rectangle are right angles;

Theorem 2, the diagonals of rectangles are equal;

It is inferred that the center line of the hypotenuse of a right triangle is half of the hypotenuse.

Second, new awards.

1, ask questions

Is the inverse proposition of (1) rectangular property theorem 1 a true proposition? According to the questions and conclusions, write what is known and verify it; How to prove it?

(2) Is the inverse proposition of the rectangular property theorem 1 a true proposition? According to the questions and conclusions, write what is known and verify it; How to prove it?

(3) What's the difference between defining a judgment rectangle and Theorem 1 and Theorem 2 in terms of condition numbers?

(4) What properties and judgments are used in the solution of Example 2? Is there any other way to get the length of the other side of the rectangle in this problem?

2. Self-study inquiry: self-study textbook P85-87, complete the preview questions and ask difficult questions.

3. Group discussion; Discuss the problems that can't be solved by self-study and the problems raised by students.

4. Feedback induction

(1) rectangle judging theorem 1: A quadrilateral with three right angles is a rectangle.

Known: in quadrilateral ABCD,? A=？ B=？ C=900，

Prove that the quadrilateral ABCD is a rectangle.

How to guide: A parallelogram with an angle of 900 is a rectangle. )

(2) Rectangular Judgment Theorem 2: Parallelograms with equal diagonals are rectangles.

It is known that in parallelogram ABCD, AC=DB,

Prove that the parallelogram ABCD is a rectangle.

(Method instruction: the adjacent angles of parallelogram are complementary, triangles are congruent and adjacent angles are equal)

(3) Summary: What is the difference between the rectangular sum theorem 1 and theorem 2 in terms of condition numbers? Definition: One of the angles is a right-angled parallelogram.

Theorem 1: Three angles are right-angled quadrangles.

Theorem 2: Parallelogram with Equal Diagonal Lines

?

Step 5 try to practice

(1) Tracking exercise1-6;

(2) standard practice 2;

(3) Example 2: Known; Diagonal lines AC and BD of parallelogram ABCD intersect at point O of triangle AOB.

Is an equilateral triangle, AB=4cm, find the area of this parallelogram.

Problem solving instruction: A: Determine the length of rectangle from Pythagorean theorem in right triangle.

B: judging the rectangle-a right triangle with 300 angles gets the length of the rectangle;

(4) Standard practice1;

(5) others;

6. Deepen innovation

Summary: What's the difference between the definition of judgment rectangle and theorem 1 and theorem 2 in terms of condition numbers?

Definition: One of the angles is a right-angled parallelogram.

Theorem 1: Three angles are right-angled quadrangles.

Theorem 2: Parallelogram with Equal Diagonal Lines

7. Recommended homework

(1) memory method, its connection and difference;

(2) Finish the exercise paper;

(3) Preview: (1) The definition of a diamond, which two conditions should it meet? ;

(2) What is the content of theorem 1 and how to prove it? ：

(3) What is the content of Theorem 2 and how to prove it? ;

(4) The area formula of diamond?

(5) What attributes and judgments are used in the solutions of Examples 3 and 4?

Tracking exercise

Is the inverse proposition of (1) rectangular property theorem 1 a true proposition? According to the questions and conclusions, write what is known and ask for proof; How to prove it?

(2) Is the inverse proposition of the rectangular property theorem 1 a true proposition? According to the questions and conclusions, write what is known and ask for proof; How to prove it?

(3) What's the difference between defining a judgment rectangle and Theorem 1 and Theorem 2 in terms of condition numbers?

(4) What properties and judgments are used in the solution of Example 2? In this problem, obtaining the length of the other side of the rectangle includes

Is there no other way?

Tracking exercise

(1) A set of quadrangles with right angles must be rectangles. ( )

(2) A set of quadrilaterals whose adjacent angles are right angles must be rectangles. ( )

(3) The quadrilateral whose diagonal bisects each other is a rectangle. ( )

(4) Diagonally complementary parallelograms are rectangles. ( )

(5) Three corners are rectangular and one corner is rectangular.

(6) Two groups of opposite sides are parallel respectively, and the quadrilateral of the diagonal is a rectangle.

Innovative practice

(1) A quadrilateral satisfying the following condition () is a rectangle.

(a) The three angles are equal; An angle is a right angle.

(c) Diagonal lines are equal and perpendicular to each other (d) Diagonal lines are equal and equally divided.

Standard exercises

(1) It is known that in the parallelogram ABCD, e is the midpoint of CD and the triangle ABE is an equilateral triangle. It is proved that quadrilateral ABCD is a rectangle.

(2) Answer: How to check whether a quadrilateral is a rectangle with a scale?

Comprehensive application exercise

It is known that the bisector of the inner corner of the parallelogram ABCD intersects with points P, Q, M and N, which proves that the quadrilateral PQMN is a rectangle.

Recommended homework

(1) memory method, its connection and difference;

(2) Finish the exercise paper;

(3) Preview: (1) The definition of a diamond, which two conditions should it meet? ;

(2) What is the content of theorem 1 and how to prove it? ：

(3) What is the content of Theorem 2 and how to prove it? ;

(4) The area formula of diamond?

(5) What attributes and judgments are used in the solutions of Examples 3 and 4?

Mathematics Teaching Strategies for Grade Eight

First, change the role of teachers and create a harmonious classroom atmosphere.

We should walk into the classroom with strong feelings, so that when we enter the classroom, we will be full of emotions, and when we board the platform, we will be full of emotions, thus achieving the effect of enlightening people's hearts and thinking. Don't be annoyed by the occasional bad phenomenon in class, especially for naughty students, let alone criticize them in class. Treat students with problems, point out their mistakes after class, then explain patiently, change with actions and emotions, and never give up. In this way, students can unconsciously accept mathematics knowledge and complete their learning tasks in relaxed, happy and harmonious emotional communication between teachers and students.

Second, carefully design the learning situation and guide students to immerse themselves in the mathematics learning situation.

The so-called creation of learning situation refers to carefully creating an immersive atmosphere for students in class, linking what they have learned with reality, and creating a realistic environment in which students can exert their imagination and better understand what they have learned. Like teaching? What is the shortest vertical line segment between dashed lines? At that time, I created a situation for students: a man unfortunately fell into the crocodile pool, but even more unfortunately, several crocodiles were swimming towards him. Students, how should he escape? The students are almost the same: swim vertically to the shore. ? In this way, students will never forget that the vertical line between the origin and the straight line is absolutely shortest. From this point of view, carefully designing the learning situation and guiding students to immerse themselves in the real situation of mathematics learning can make students immerse themselves in the real situation of mathematics learning and master the knowledge they have learned better and more solidly.

Third, guide students to learn the law.

In primary school, students usually study mathematics under the guidance of teachers, while primary school students have shallow knowledge of mathematics, less things to understand and less difficulty in learning. But in junior high school, there are more and more subjects and the content is becoming more and more difficult. A lot of knowledge focuses on understanding, and students are at a loss for a while. This requires our math teacher to guide us in learning methods. So, how to guide students to study law? First of all, we should help students make study plans. Because they are young and lack a clear and scientific study plan, our teacher should help them make corresponding and appropriate study plans according to the learning situation of different students. Secondly, students should be given repeated and specific guidance, training and reinforcement in the methods of listening to lectures, previewing, reviewing, reading and memorizing. Thirdly, we should also pay attention to the connection of primary and secondary school knowledge in teaching, so that students can learn step by step, establish learning confidence and stimulate learning interest. Finally, students may have left some bad study habits in primary school. Teachers should constantly observe and discover their study habits, correct and guide them, help them get rid of bad study habits, establish a good study attitude and form scientific study habits. Only by instructing students on learning methods and how to learn mathematics better can teachers give students a correct direction and make it easier for them to obtain good learning results.

Fourth, the use of multimedia teaching.

With the development of information technology, multimedia technology has spread to all aspects of society and is widely used in classroom teaching. Multimedia teaching has its remarkable characteristics: first, it can effectively increase the class capacity of each class; The second is to reduce the workload of teachers writing on the blackboard, so that teachers can have the energy to explain examples in depth and improve the efficiency of explanation; Third, it is intuitive, easy to stimulate students' interest in learning, and conducive to improving students' initiative in learning; Fourth, it is helpful to review and summarize what the whole class has learned. At the end of class, the teacher guides the students to summarize the content of this lesson and the key and difficult points, and at the same time, the content will jump synchronously through the projector? Open the classroom curtain, so that students can further understand and master the content of this lesson. We have analyzed many advantages of multimedia teaching, which is also the reason why multimedia teaching is widely used now. In fact, most schools and classrooms will use multimedia for teaching. Therefore, in order to improve the efficiency of junior high school mathematics teaching, it is inevitable to use multimedia to teach and improve the efficiency of mathematics teaching. At the same time, teachers should also pay attention to moderation and appropriateness when using multimedia in teaching, and pay attention to the communication and interaction between teachers and students. Only in this way can we not violate the original intention of multimedia teaching.

Verb (abbreviation of verb) conclusion

Above, we have analyzed various methods to improve the efficiency of junior high school mathematics teaching from four aspects: classroom atmosphere, students' interest, teaching methods and means. These are the most important and basic methods to improve the teaching effect. However, due to the limited space, there are certainly many methods that we haven't mentioned, such as preparing lessons, assigning homework, and evaluating students' differentiated teaching and learning, all of which need our constant exploration and efforts. Only by being a conscientious teacher can we achieve ideal teaching results and promote the improvement of students' academic performance and the all-round development of their quality.

Author: Zhang Bin Unit: Xiongjiachang Middle School, zhijin county, Guizhou.

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