This section focuses on the inverse theorem of Pythagorean theorem and its application. It can judge whether a triangle is a right triangle by the relationship of sides. It provides a powerful basis for judging the shape of triangle.

The difficulty of this section is the application of the inverse theorem of Pythagorean theorem. When using the inverse theorem of Pythagorean theorem, it is not clear which side is the hypotenuse, so it is wrong to judge the shape of triangle with the inverse theorem of Pythagorean theorem. In addition, it is also difficult for students to change the quantitative relationship of a given edge through algebra and finally get an objective formula when solving related comprehensive problems.

Teaching suggestions:

The teaching mode of this class mainly adopts "interactive" teaching mode and "analogy" teaching method. Through the middle vertical theorem and its inverse theorem, make analogy, let students ask questions and solve problems by themselves. Create a relaxed and lively classroom atmosphere in classroom teaching. Cultivate students' thinking ability through teacher-student interaction, student-student interaction and student-textbook interaction. Specific instructions are as follows:

(1) Let the students ask questions.

Using analogy learning method, students will write the inverse proposition of Pythagorean theorem learned in the last class. Students are required to dictate words separately here; Write the content of the inverse proposition on the blackboard in the form of symbols and figures. These are all made by students themselves, so it is estimated that students will not find it difficult. This design is mainly to cultivate students' habit and ability of asking questions.

(2) Let students solve problems by themselves.

Judge whether the above inverse proposition is true? Students will find it difficult to solve this problem. Here, teachers can give appropriate guidance, but they should try their best to let students discover and explore and find solutions to problems.

(3) Cultivate students' mathematical consciousness by solving practical problems.

Teaching objectives:

1, knowledge target:

(1) Understand and prove the inverse theorem of Pythagorean theorem;

(2) The inverse theorem of Pythagorean theorem will be applied to determine whether a triangle is a right triangle;

(3) Know what Pythagorean numbers are and remember some perceptual Pythagorean numbers.

2, ability goal:

(1) Improve students' discrimination ability by comparing Pythagorean theorem and its inverse theorem;

(2) Combine Pythagorean Theorem and previous knowledge for comprehensive application to improve the comprehensive application ability of knowledge.

3, emotional goals:

(1) The feeling of gaining mathematical knowledge through the development experience of autonomous learning;

(2) Feel the dialectical characteristics of mathematics through the vertical knowledge and lateral transfer.

Teaching Emphasis: The Inverse Theorem of Pythagorean Theorem and Its Application

Teaching Difficulties: Inverse Theorem of Pythagorean Theorem and Its Application

Teaching tools: ruler, microcomputer

Teaching method: student-centered. Discuss the exploration method.

Teaching process:

1, background knowledge review of new lesson (projection)

Content of Pythagorean Theorem

Text narration (projection display)

Symbolic type

Graphics (drawn on the blackboard)

2. Get the inverse theorem

(1) Ask students to express the inverse proposition of the above theorem in written language.

(2) The students themselves prove that

Inverse theorem: If the lengths of three sides of a triangle have the following relationship:

So this triangle is a right triangle.

Emphasize the difference between (1) Pythagorean theorem and its inverse theorem.

Pythagorean theorem is the property theorem of right triangle, and the inverse theorem is the judgment theorem of right triangle.

(2) the method of judging right triangle:

① Angle is right angle, ② vertical, ③ Inverse theorem of Pythagorean theorem.

2. Application of Theorem (on the topic of projection display)

Example 1 known: As shown in the figure, in quadrilateral ABCD, ∠B=, AB=3, BC=4, CD= 12, AD= 13, find the area of quadrilateral ABCD.

Example 2 is shown in the figure. As we all know, CD⊥AB is in Zone D, and

It is proved that △ACB is a right triangle.

The above examples are thought by students first and then answered. Teachers and students complement each other. (The teacher makes a summary)

4, class summary:

The common mistake in the application of (1) inverse theorem is that it is not clear which side is the hypotenuse (the largest side).

(2) A method to judge whether it is a right triangle: combining Pythagorean theorem, algebraic formula and equation.

5. Task:

I. Written assignment P 13 1#9

B. Hand-in homework: known: as shown in the figure, in △DEF, DE= 17, EF=30, DG=8 beside EF.

Prove that △DEF is an isosceles triangle.

Design of blackboard writing: (omitted)