[Textbook Analysis].
The "Determination of Parallel Lines (1)" designed in this lesson is the content of the second section of Chapter 5 of the second volume of the seventh grade of the People's Education Edition of "Mathematics", and the method of judging two straight lines in parallel is mastered. Learning the content of parallel judgment is not only the foundation and the only way for the content of "Space and Graphics", but also the necessary for students to accumulate experience in space and graphics, master the basic knowledge of plane graphics, and learn simple and preliminary reasoning and reasoning. Through the learning of this section, students can develop hands-on, active, cooperative and communication skills. By combining the occurrence and development process of display knowledge, students are encouraged to think and summarize, so as to cultivate students' good learning habits and thinking quality.
【Teaching Objectives】
1) From the activity process of "drawing parallel lines with a triangular ruler and a ruler", it is found that the isotopic angle is equal and the two straight lines are parallel, which cultivates students' hands-on operation, initiative and cooperation and communication ability.
2) Be able to use the method of judging parallel lines to determine the parallelism of two straight lines, and initially learn to use geometric language for simple reasoning and expression.
3) Let students experience the joy of exploration, communication, success and improvement in the activities, stimulate students' interest in learning mathematics, and cultivate students' scientific attitude of daring to practice bold conjectures and reasoning. Teaching Focus: Difficulty:
【Teaching Focus】Three judgment methods and application teaching of two straight lines in parallel.
[Teaching difficulties].Derivation of three judgment methods with two parallel lines.
[Teaching Preparation].Triangles, courseware.
[Teaching process].
1. Scenario import.
If strip B is perpendicular to the edge of the wall, what degree is the angle between strip A and the edge of the wall to make strip A parallel to strip B?
To solve this problem, it is necessary to figure out the parallel judgment.
2. The condition that the straight line is parallel.
In the past, we have learned to draw parallel lines with a ruler and a triangular ruler, as shown in the figure (Textbook P13, Figure 52-5) What hasn't changed during the movement of the triangle?
The angle of the triangle through the edge of the point p and the edge against the ruler does not change.
Simplifying Figure 52-5, Figure 3
1 and 2 are the positions of the triangle before and after the angle formed by the edge of the point p and the edge leaning on the ruler, obviously 1 and 2 are at the same angle and they are equal, from this we can know?
The two straight lines are truncated by the third straight line, and if the isotopic angles are equal, then the two straight lines are parallel.
To put it simply: the isotope angles are equal, and the two straight lines are parallel.
Symbolic language: 1= 2 ab cd
As shown in the figure (textbook p145.)2-7) Can you tell the story of how the carpenter draws parallel lines with a tool called a ruler in the diagram?
Drawing parallel lines with an angle ruler is actually drawing two right angles, according to the principle of "equal angles, two straight lines are parallel." It can be seen that the parallel lines are drawn in this way.
As shown in the figure, (1) if 2 = 3, can a b be obtained? (2) If 2 4 1800, can a b be obtained?
Can you summarize the above conclusion in words?
The two straight lines are truncated by the third straight line, and if the inner wrong angles are equal, then the two straight lines are parallel.
To put it simply: the inner misalignment angles are equal, and the two straight lines are parallel.
Symbolic language: 2= 3 a b
2) 4 + 2 = 180°, 4 + 1 = 180° (known).
2 = 1 (the complementary angles of the same angle are equal).
a∥b.(The isotope angles are equal, and the two straight lines are parallel).
Can you summarize the above conclusion in words?
The two straight lines are truncated by the third straight line, and if the inner angles of the same side are complementary, then the two straight lines are parallel.
To put it simply: the same side inner angles are complementary, and the two straight lines are parallel.
Symbolic language: 4+ 2=180° a b
Design intent: With the help of the process of drawing parallel lines with a ruler and a triangle, the condition that the straight lines are parallel is obtained. Through learning, students will further master the judgment method and application of two parallel lines.
3. Classroom exercises.
1. Textbook P15 Exercise 1, Supplement (3) Which two straight lines can be judged by A+ ABC 1800? On what basis?
2. P162 questions in the textbook.
4. Class summary: How to judge that two straight lines are parallel?
5. Assignment: P questions;
[Teaching Reflection].
The main content of this section is the method of judging parallel lines, which is also the focus of this chapter, the method of using the same angle to determine the parallel lines of two straight lines is given, when drawing parallel lines, the triangular ruler moves close to the ruler, the size of the triangular ruler remains the same, that is, the isotopic angle is equal, the use of the inner wrong angle and the same side of the inner angle to determine the parallel of the two straight lines, I use the textbook problem method, through analysis, guide students to discover the relationship between these angles, and ask students to complete it themselves, students in the derivation method twoI always think that at this time it is known that the isotope angle is equal, rather than being proved by simple reasoning, which I am very confused about, and I have emphasized it before, but it has little effect, and when the student deduces method three, it is much better, and method one or method two can be used to get method three.