The seventh grade mathematics courseware: the nature of parallel lines

The seventh grade mathematics courseware: the nature of parallel lines;

1. Make students master three properties of parallel lines and use them for simple reasoning.

2. Make students understand the nature of parallel lines and the difference between judgment.

Key points and difficulties:

The three attributes of 1. parallelism are the focus of this section and one of the focuses of this chapter.

2. How to distinguish between nature and judgment is a difficult point in teaching.

Teaching process:

First, consolidate old knowledge and introduce problems.

Consolidating the judgment method of parallel lines and guiding students to analyze the judgment of parallel lines is to draw parallel conclusions according to the relationship between some angles. On the basis of students' analysis, this paper puts forward that if the conditions and conclusions in the judgment are exchanged, whether it is possible to draw some angle relations such as "the same angle is equal" from "two straight lines are parallel" and thus introduce the topic.

Second, experimental verification and characteristic exploration.

1. The horizontal grid of windows in the classroom is parallel. Please watch the teacher check a pair of isosceles angles with a triangular ruler and see what the result is. The teacher demonstrated on the window with a triangular ruler, and the students observed and thought. )

2, student experiment (print parallel pages)

(1) Given a//b, draw a straight line C at will and intersect with parallel lines A and B. 。

(2) Choose a pair of isosceles angles and experiment with appropriate methods to see what the relationship between these two isosceles angles is.

Let students draw more cross sections and try, and encourage students to explore in various ways.

3. Experimental conclusion:

Two parallel lines are cut by a third straight line and have the same angle.

The abbreviation is "two straight lines are parallel and the same angle is equal"

Remember this property and discuss what is known and what is the conclusion in this feature. What's the difference between it and "the same angle is equal and two straight lines are parallel"?

4, problem discussion:

We know that two parallel lines are cut by a third line, which not only forms an isosceles angle, but also forms an internal dislocation angle and an internal homoclinic angle. We already know that "two parallel lines are cut by a third line, and the isosceles angles are equal". Then please think about it: when two parallel lines are cut by a third straight line, what is the relationship between the internal dislocation angle and the internal homoclinic angle?

As shown in the figure, what is the relationship between given straight lines A/B, ∠ 1 and ∠2, ∠2 and ∠3? Why?

Group discussion, giving enough time to communicate, can guide students.

Compare from the same angle, and draw a conclusion, pay attention to the students in

Can you think about this positively and methodically?)

Conclusion: "The two straight lines are parallel and the internal dislocation angles are equal"

"These two straight lines are parallel and complementary."

Remember these two properties, think about what conditions you know and what conclusions you draw, which are different from "the internal angles are equal and the two lines are parallel" and "the internal angles on the same side are complementary and the two lines are parallel".

5. Summarize three properties and three judgments of parallel lines.

Third, case study and practical application.

(1) Find one.

Example: As shown in the figure, AD∨BC, AB∨DC, ∠ 1= 100, find the degree of ∠2, ∠3.

(2) do:

As shown in the figure, a beam of parallel rays AB and DE are reflected after being photographed on a horizontal mirror. At this time ∠ 1=∠2, ∠3=∠4,

What is the relationship between the size of (1)∠ 1 and ∠3? ∠2 and ∠4

(2) Are the reflected rays BC and EF parallel?

First, let students answer and reason in their own language, and then show the following reasoning process. Students explain the reasons for each step.

(3) Test you:

The picture shows a trapezoidal jade unearthed from the world-famous Sanxingdui Archaeology. The staff has detected ∠A= 1 15 and ∠D= 100 from the jade piece. Given two bases of a trapezoid, please find the degrees of the other two angles.

Students try to write the reasoning process in their own way.

(4) Fill in the blanks:

Known: As shown in the figure, ∠ADE=60, ∠B=60, ∠C=80.

Q∠AED is equal to how many degrees? Why?

∠∠ADE =∠B = 60 (known)

∴de//bc(_______________________________________)

∴∠aed=∠c=80(____________________________________)

(Fill in the blanks to test students' judgment on parallel lines and distinguish their properties. )

Fourth, the class summary:

1. What are the three properties of parallel lines?

2. The difference between the nature of parallel lines and the judgment of parallel lines:

Judgment: The relationship between angles is parallel.