What are the common topics in junior high school math teacher recruitment interview lectures? The textbook is Su Ke Edition.

1 1.2. 1 triangle congruence judgment (SSS)

I. Teaching content

The main content of this lesson is to explore the condition of triangle congruence (SSS) and prove it with congruent triangles.

Second, the teaching objectives

Knowledge and skills

In order to understand the stability of triangles, we will use "edge" to determine the congruence of two triangles.

(2) Process and method

Through exploring "side by side", we can experience the process of judging congruent triangles and solve simple problems.

(3) Emotion, attitude and values

Cultivate organized thinking and expression skills, and form a good sense of cooperation.

Three. Key points, difficulties and key points

(1) key point: master the method of "edge-edge" to judge the congruence of two triangles.

(2) Difficulties: Understand the basic process of proof and learn the comprehensive analysis method.

(c) Key: Grasp the graphic features and find two triangles suitable for conditions.

Fourth, the preparation of teaching AIDS.

A piece of cardboard, a ruler and a compass, the shape is as shown in figure 1.

Verb (abbreviation of verb) teaching method

Using the teaching method of "operation-experiment", students do it themselves and form an intuitive image.

Sixth, the teaching process.

(A) set up problems, solve problems, improve operational awareness

Teacher activities (display of teaching AIDS)

Problem: After a piece of triangular glass is damaged, only the fragments as shown in Figure 2 remain. What measurement do you make for the fragments in the picture? You can cut out the triangle glass that meets the specifications and communicate with your partner.

Students can observe, think and answer teachers' questions. The method is as follows: You can put the glass fragments of the figure 1 on a piece of cardboard, and then draw a complete triangle with a ruler and pencil or ink. As shown in Figure 2, the glass can be cut after the template is cut.

Theoretical cognition

If △ ABC △ a ′ b ′ c ′, then their corresponding edges are equal and their corresponding angles are equal. On the other hand, if △ ABC and △ A ′ B ′ C ′ satisfy that three sides are equal and three angles are equal, that is, AB = A ′ B ′, BC = B ′ C ′, and CA = C ′ A ′.

These six conditions can guarantee △ ABC△ a ′ b ′ c ′. From the practice just now, we can find that as long as the three sides corresponding to two triangles are equal, we can ensure that these two triangles are congruent.

Believe it or not?

Drawing verification (using ruler and compass)

Draw a △ABC at will, and then draw a △ a ′ b ′ c ′, so that a ′ b ′ = ab, b ′ c ′ = BC, and c ′ a ′ = ca. Cut the drawn △ A ′ B ′ C ′ and put it on △ABC. Can they completely overlap? (that is, congruence? )

Students take out rulers and compasses and draw and verify them according to the above requirements (as shown in the textbook drawing 1 1.2-2).

Draw a △ a ′ b ′ c ′ so that a ′ b ′ = ab ′, a ′ c ′ = AC, b ′ c ′ = BC:

1. Draw a line segment with b' c' = BC;

2. Draw an arc with B' and C' as the center and segments AB and AC as the radius respectively, and the two arcs intersect at point A';

3. Connect line segments A ′ b ′, A ′ c ′.

Teachers patrol and guide activities, introducing the topic: "What laws are reflected by the above life examples and ruler drawing results?"

On the basis of thinking and practice, students' activities can sum up the following theorems to judge the congruence of two triangles.

(1) Judgment method: three sides correspond to the congruence of two equal triangles (abbreviated as "side" or "SSS").

(2) The reasoning process of judging the congruence of two triangles is called proving the congruence of triangles.

Through the whole process of drawing, observing, comparing and communicating, students gradually explore the final conclusion-edge edge. In this process, students not only get the condition that two triangles are congruent, but also enhance their mathematical experience.

This article comes from: Chinese public teacher examination network detailed source reference: