: congruent triangles
Teaching objectives
① Understand the concept and characteristics of congruence through examples, and know the congruence of graphics.
② Knowing the related concepts of congruent triangles, we can correctly find out the corresponding vertex, corresponding edge and corresponding angle; Master the properties that congruent triangles's corresponding edges are equal and corresponding angles are equal.
(3) can use properties for simple reasoning and calculation, and solve some practical problems.
④ By changing the position of one of the two overlapping triangles, activities in different positions can be presented, so that students can understand and appreciate the idea of graphic transformation, and gradually cultivate the consciousness of dynamically learning geometric figures.
Teaching emphases and difficulties
Focus: congruent triangles's related concepts and properties.
Difficulties: Understanding the angular correspondence of congruent triangles.
Teaching design
Problem situation
1. Show many pictures in life.
Fragment 1: pattern.
Part II: Three modes on page 90 of the textbook.
2. Students discuss:
1 What do you feel from the above clip?
Can you give some similar examples in life?
Students discuss and think in groups.
1. What are the characteristics of these graphs?
2. Some people use the word "conformal" to describe the above picture. What do you think this word means? Teachers know that. Build a model
1. Give the definitions of congruence and congruent triangles.
2. List counterexamples and emphasize the conditions of definition.
3. Ask the question "Can you construct a pair of congruent triangles"? How do you organize and communicate with your colleagues?
4. Corresponding elements and properties of congruent triangles: Teachers use teaching AIDS in their hands to explain the meanings of vertices, edges and corners of corresponding elements, and guide students to observe the relationship of corresponding elements in congruent triangles, and find that corresponding edges are equal and corresponding angles are equal. Teachers inspire students to explain the truth according to "coincidence".
Analysis, application and expansion
1. Taking two triangles in figure 13. 1- 1 as examples, this paper introduces the symbolic representation, reading and writing, and congruence of the corresponding edges and angles of the two triangles, and tells the figures 13. 1-2 and/.
2. Summarize the method of finding congruent triangles's corresponding elements, and permeate the idea of congruent transformation.
3. Using two self-made congruent triangles templates, students independently spell out five figures on pages 92-93 of the textbook by translation, folding and rotation, and tell their corresponding vertices, edges and angles, and then communicate with their peers. Can you spell other numbers?
Expansion and extension
1. Example1△ ABC △ dfe, ∠ A = 96, ∠ B = 25, DF= 10cm. Find the degree of e and the length of AB.
Classroom practice
Attention: Check the students' mastery of this lesson.
1. congruence is indicated by the symbol _ _. It is pronounced _ _.
2.△ABC is all equal to triangle △DEF, which is expressed as _ _.
3. △ ABC △ def and ∠A correspond to ∠D and ∠B are ∠E, then ∠C and _ _ are corresponding angles; AB and _ _ are corresponding edges, BC and _ _ are corresponding edges, and AC and _ _ are corresponding edges.
4. True or false:
1 congruent triangles has equal sides and angles.
The circumference of congruent triangles is equal.
A triangle with equal area is congruent triangles.
Congruent triangles have equal areas.
5. Find congruent triangles in the jigsaw puzzle.
Nodular improvement
1. Think back to this lesson: What knowledge did you get from congruent triangles in your own practice? Note: Teachers should give positive comments on students' speeches.
2. Find the corresponding elements of congruent triangles, and pay attention to the hidden conditions in the graph, such as common elements and antipodal angles. , but the male vertex is not necessarily the corresponding vertex;
3. When applying the definition and nature of congruent triangles, we should pay attention to the standardization of writing format.
arrange work
1. Required questions: Exercise on page 92 of the textbook 13. 1, 2, 3.
2. Choose the problem: Exercise on page 92 of the textbook 13. 1.
Teaching postscript
: the condition of triangle congruence 1
Teaching objectives
① Experience the process of exploring the congruence condition of triangle and realize the process of drawing mathematical conclusions through operation and induction; ② Grasp the "edge-edge" condition of triangle congruence and understand the stability of triangle.
③ Cultivate students' cooperative spirit by discussing problems together.
Teaching emphases and difficulties
Key points: guide students to analyze problems and find conditions for judging triangle congruence.
Difficulties: the exploration process of triangle congruence conditions.
Teaching design
Review the process and introduce new knowledge.
Lead the students to review the definition and nature of congruent triangles, and draw the conclusion that congruent triangles has three equal sides and three equal angles. On the other hand, these six elements are equal, so the two triangles must be congruent.
Create situations and ask questions
According to the above conclusions, the question is raised: Do two triangles have congruences, and do six conditions have to be met? If only some of the above six conditions are met, can two triangles be guaranteed to be congruent?
Organize students to discuss and communicate. After the students' step-by-step analysis, all kinds of situations gradually became clear and summarized.
Build models, explore and discover
Display inquiry 1, draw a △ABC at will first, and then draw a △A'B'C' to make △ABC and △A'B'C' meet one or both of the above conditions. Are the △A'B'C and △ABC you drew necessarily the same?
Let the students make triangles according to the conditions given below.
The two angles of the 1 triangle are 30 and 50 respectively.
The two sides of the triangle are 4 cm and 6 cm respectively.
One angle of a triangle is 30 and one side is 3 cm.
By drawing, cutting and comparing, it is concluded that when only one or two conditions are given, the drawn triangle cannot be guaranteed to be congruent.
Display query 2. Draw a △A'B'C at will, so that A'B'=AB, B'C'=BC, C'A'=CA. Cut out the drawn △A'B'C and put it on △ABC. Are they the same?
Through communication, we can draw such a conclusion:
Three sides correspond to two equal triangles.
At the same time, it is also clear that three conditions are needed to judge the congruence of triangles.
Apply new knowledge and experience success.
Physical demonstration: a triangular frame made of three pieces of wood with fixed size and shape.
Let students understand the stability of triangle through physical objects. Encourage students to cite examples from life.
Note: Let students experience the extensive application of mathematics in life.
Give an example 1, as shown in the figure △ABC is the steel frame, AB=AC, and AD is the connection point A..
Verify △ Abd △ ACD with brackets in the middle of BC.
Consolidation exercise
Thinking and practice of 96 pages of teaching material.
Reflection summary
Master the laws of mathematics.
Infiltrate the mathematical thought of classification again, experience the method of analyzing problems, and accumulate the experience of mathematical activities. homework
1. Required questions: 1 and 2 questions on page 103 of the textbook 13.2.
2. Choose the topic: Question 9 on page 104 of the textbook.
Teaching postscript
: Condition 2 of triangle congruence
Teaching objectives
① Experience the process of exploring the congruence condition of triangle, and cultivate students' ability to observe and analyze graphics and practice. ② In the process of exploring the congruence condition of triangle and its application, we can think methodically and reason simply.
③ Cultivate students' cooperative spirit by discussing problems together.
Teaching emphases and difficulties
Key point: Use "edge" to prove that two triangles are congruent, and then get that the line segments or angles are equal. Difficulties: guide students to analyze problems and find conditions for judging the congruence of triangles.
Teaching design
Create situations and introduce topics.
Display query 3: Given any △ABC, draw △A'B'C' so that A'B'=AB, A'C'=AC, ∠ A' = ∠ A
The teacher instructs the students to draw while learning, and then asks them to cut out the drawn δ A 'b 'c' and put it on δδABC to see if the two triangles are congruent.
Exchange dialogues and explore new knowledge.
According to the previous operation, encourage students to summarize the rules in their own language:
A triangle with two sides and their included angles equal. Scandinavian airlines
Attention: Cultivate students' generalization ability and language expression ability.
Additional emphasis: the angle must be the included angle of two equal corresponding sides, and the side must be two opposite sides with equal angles. Note: The laws obtained by inductive analysis enable students to have a deeper understanding.
Apply new knowledge and experience success.
Example 2, as shown in the picture, has a pond. To measure the distance between the two ends of the pond, you can first take a point C on the flat ground that can go straight to A and B, connect AC and extend to D, so that CD=CA, BC and E, and CE=CB. Connect DE, then the length of DE is the distance between A and B, why?
Explore again and solve the problem.
Showing Inquiry 4, we know that two triangles with equal included angles are congruent. Can two triangles be judged to be congruent on the condition that "two sides are equal to one diagonal"? Why?
Let the students imitate the previous inquiry method and draw the conclusion that two triangles with equal diagonal lines on both sides and one of them is not necessarily the same.
Teacher's demonstration: Method 1: 98-page textbook, figure 13.2-7.
Method 2: Draw pictures to make students draw conclusions more intuitively.
Consolidation exercise
Page 99 of the textbook, exercise 12.
summary
1. Method for judging triangle congruence;
2. What are the common methods to prove that line segments and angles are equal? Let students express freely, other students supplement, and let students systematize their knowledge and construct it in their own way.
Note: Through the class summary, summarize and sort out the content of this lesson to help students improve their cognitive structure and form problem-solving experience.
homework
1. Required questions: textbook page 104, exercises 13.2, questions 3 and 4.
2. Topic: The textbook page 105, question 10.
Teaching postscript