I. teaching material analysis

(A) the status and role of teaching materials

Similar triangles's knowledge was expanded and developed on the basis of congruent triangles's knowledge. Similar triangles inherited congruent triangles's knowledge and deepened it from special equality to general proportion, so as to learn similar triangles's knowledge well and lay a good foundation for further study of trigonometric functions and proportional line segments related to solids.

This lesson is to prepare for learning similar triangles's judgment theorem, so learning this lesson well is very important for future study.

(B) Teaching objectives and requirements

1. Knowledge Objective: Understand similar triangles's concept and master the preliminary theorem for judging triangle similarity.

2. Ability goal: train students to explore new knowledge, improve their ability to analyze and solve problems, enhance their ability of decentralized thinking, and extend the existing knowledge field to the nearest development field.

3. Emotional goal: strengthen students' interest in knowledge inquiry and infiltrate rational thinking into geometry.

(C) the focus and difficulty of teaching

1. Emphasis: the concepts of similar triangles and similarity ratio and the preliminary theorem for judging triangle similarity.

2. Difficulties: the definition of similar triangles and the preliminary theorem of judging triangle similarity.

Second, teaching methods and learning methods.

Using the method of intuitive analogy and multimedia-assisted teaching, we can guide students to preview the contents of textbooks, form good self-study habits, inspire students to find and think problems, and cultivate students' logical thinking ability. Gradually doubt, guide students to actively participate in the discussion, affirm their achievements, make students feel a sense of accomplishment, and improve their interest and enthusiasm in learning.

Third, the analysis of the teaching process

Look at the national flag of China. The big five-pointed star and the small five-pointed star on the national flag are similar figures. The new knowledge to be learned in this class is similar triangles, which is prepared in four steps.

1. Learning similar triangles's definition is to sum up two conditions of definition from practice, cultivate students' thinking methods of observation and induction, and transform perceptual knowledge into rational knowledge. I'm going to introduce the midline theorem of triangle, so that students can draw a triangle with the midline of triangle, and then ask: What is the relationship between the triangle cut by the midline of triangle and the angle of the original triangle? What does each party have to do with it? Then move up and down from the straight line where the center line is, and think about how to answer. Students can easily draw a conclusion from what they have learned: "The angle of the cut triangle is equal to the angle of the original triangle, and the corresponding side is proportional." Finally, two triangles with these two characteristics are called similar triangles. This teaching method is designed to cultivate students' practical ability and observation ability. And gradually cultivate inductive thinking ability from concrete to abstract. Move the cut triangle out as △ABC and the original triangle out as △A'B'C'. Therefore, if there is:

∠A=∠A '，∠B=∠B '，∠C=∠C '，

Then △ABC is similar to △A'B'C' to strengthen the understanding of the similar definition of two triangles.

2. When the similarity symbol "∽" indicates that two triangles are similar, it is considered that the analogy with the congruence symbol ""in congruent triangles is introduced. The congruent symbol "≦" can be regarded as a combination of the symbol ""with the same shape and the symbol "=" with the same size, but only the symbol ""is used to represent the symbols with similar shapes. This statement is the visualization of lattice mathematical symbols. It's easier for students to remember. Please give us your advice. It must be noted that the similarity symbol "∽" indicates that two triangles are similar, and the corresponding vertices should be written at the corresponding positions when writing. For example, two similar triangles, if vertex D corresponds to A, E corresponds to B and F corresponds to C, should be written as △ABC∽△DEF, but not as △ABC∽△FDE at will. The problem of writing the corresponding vertex in the corresponding position often shows its importance in solving problems in the future. According to the definition of the similar triangles Covenant:

If two triangles are similar, then their corresponding angles are equal, reaching corresponding proportions. When judging their corresponding corners and edges by similarity, if their corresponding items are written according to the corresponding positions, then this judgment is accurate and rapid. If △ABC∽△DEF, AB, BC and AC correspond to DE, EF and DF respectively, while △ A, △ B and △ C correspond to △ D, △ E and △ F respectively. In this way, confusion and mistakes can be avoided. It is also a kind of thinking method training for students, guiding students to be organized and organized when considering problems. When judging the corresponding edge and corresponding angle of similar triangles, another method is often used, that is, the edge corresponding to the angle is the corresponding edge. The included angle of the corresponding side is the corresponding angle.

3. About the teaching of the concept of similarity ratio, let students know that if two triangles are similar, the ratio of one side of the first triangle to the corresponding side of the second triangle is called the similarity ratio (or similarity coefficient) of the first triangle and the second triangle. We must pay attention to the sequence and corresponding problems here. For example: △ABC∽△DEF, then it is the similarity ratio of △ABC and △DEF, but refers to the similarity ratio of △DEF and △ABC, and these two similarity ratios are reciprocal. This shows that congruent triangles is a special case of similar triangles when the similarity ratio is equal to L.

4. Before teaching the preliminary theorem, you can review the conclusion of Example 6 on page P2 15 of last class [The triangle cut by a straight line whose three sides are parallel to one side of the triangle and intersect with the other two sides is proportional to the three sides of the original triangle. For the derivation of the proposition, you can draw a triangle first, and then draw a straight line parallel to one side and intersecting with the other two sides, so that students can intuitively get that the cut triangle is similar to the original triangle, thus leading to the proposition that "the straight line parallel to one side of the triangle intersects with the other two sides (or extension lines on both sides), and the triangle formed is similar to the original triangle". That is, as shown in the figure, if DE∨BC, then △ADE∽△ABC, and then the conclusion of analyzing the lifeline problem is to prove that the two triangles are similar. You can ask students:

When there is no agreement to judge the similarity of two triangles, what method should be considered to prove the similarity? If you get the most valuable fruit and prove it by definition, what should you prove it from? Then give proof according to the content of the textbook. Emphasize that the first term of each ratio is three sides of the same triangle, and the last term of each ratio is three sides of another triangle. The position cannot be written wrong.

So we can get the (preliminary) theorem:

Theorem A straight line parallel to one side of a triangle intersects the other two sides (or extension lines of both sides), and the triangle formed is similar to the original triangle.

Starting from the content of teaching materials, students' spontaneous learning can be initiated, and their exploratory thinking can be guided to achieve their knowledge goals. In order to consolidate the knowledge learned in this section, arrange classroom exercises, then ask questions and adjust the board to understand the students' mastery of knowledge.

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