Teaching process:
First of all, ask questions:
(1) How to judge whether a triangle is an equilateral triangle?
(2) What conditions can an isosceles triangle meet to become an equilateral triangle?
(3) Do you think an isosceles triangle with equal angles is an equilateral triangle? Can you prove your conclusion?
Second, do it.
What kind of triangle can you make with two triangular rulers with angles? Can you spell an equilateral triangle? Tell me your reasons.
Question: What does the pendulum above remind you of? In a right triangle, what is the relationship between the right side and the hypotenuse? Can you prove your conclusion?
Theorem: In a right triangle, if an acute angle is equal to, then the right side it faces is equal to half of the hypotenuse.
Course summary:
This lesson is based on congruent triangles's judgment and the study of the nature, judgment and inference of isosceles triangle. Through the transfer of old and new knowledge and simple pendulum experiment, the theorem is intuitively explored: an isosceles triangle with an angle equal to an equilateral triangle; And theorem: in a right triangle, if an acute angle is equal to, then its right side is equal to half of the hypotenuse. These two theorems play a positive role in simplifying geometric steps and calculating or proving.
Homework:
Textbook exercise 1.3 1, 2,3
2. Right triangle (1)
Teaching objectives:
Knowledge and skills objectives:
1. Master the method of reasoning and proof, and develop students' preliminary deductive reasoning ability.
2. Further master reasoning proofs and methods, and develop deductive reasoning ability.
Process and method objectives:
1 has gone through the process of exploration, speculation and proof. Learn to prove it with this theorem.
2. Understand the proof method of Pythagorean theorem and its inverse theorem.
Emotional attitude and value goal;
1. Cultivate students' comprehensive analytical ability, geometric expression ability and good habit of actively participating in exploration activities, and experience the application of mathematical conclusions in practice.
2. Understanding the concept of inverse proposition with concrete examples will identify two mutually inverse propositions and know that the original proposition is true, but its inverse proposition is not necessarily true.
Key points, difficulties and key points:
1. Focus: master the methods of reasoning and proof, and improve thinking ability.
2. Difficulties: reasoning proof of Pythagorean theorem and inverse theorem, description of inverse proposition.
3. Key points: master deductive reasoning thinking and make full use of axioms and learned theorems to demonstrate. For the inverse proposition problem, students should verify the correctness of the inverse proposition through practical examples.
Teaching process:
Discussion:
Observe the following three groups of propositions. What do their conditions have to do with the conclusion?
If two angles are diagonal, they are equal.
If two angles are equal, they are diagonal.
If Xiaoming has pneumonia, he must have a fever.
If Xiaoming has a fever, he must have pneumonia.
The equilateral sides of a triangle face equal angles.
Equiangular faces in a triangle are equilateral.
3. Reciprocity propositions and theorems.
(1) In two propositions, if the conditions and conclusions of one proposition are those of the other, then these two propositions are called reciprocal propositions, and one of them is called the inverse proposition of the other.
(2) A proposition is true, but its inverse proposition is not necessarily true. If the inverse proposition of a theorem is proved to be true, it is also a theorem. These two theorems are called reciprocal theorems, and one theorem is called the inverse theorem of the other theorem.
Classroom exercises:
1. Write the inverse proposition of the proposition "If two rational numbers are equal, their squares are equal" and judge whether it is a true proposition.
2. Try to give some other examples.
3. Classroom exercises 1
Course summary:
What have you mastered in this course?