Congruent triangles, primary school mathematics courseware.
First, the teaching objectives
Knowledge and skills
Master the "corner edge" condition of triangle congruence and transform "corner edge" into "corner edge". Can use congruent triangles's conditions to solve simple reasoning and proof problems.
Process and method
Experience the process of exploring the congruence condition of triangle and the process of drawing mathematical conclusions through operation and induction.
Emotions, attitudes and values
In the process of exploration, induction and demonstration, we can realize the rigor of mathematics and the happiness of success.
Second, the difficulties in teaching
Teaching focus
Discussion on congruence of "corner edge" triangle.
Teaching difficulties
Transform the congruence condition of triangle "angle" into the congruence condition of triangle "angle".
Third, the teaching process
(A) the introduction of new courses
By reviewing the old judgment theorem of triangle "angle and angle": two triangles with equal angles and sides (can be abbreviated as "angle and angle" or "ASA")
(4) Summarize the homework
Question: What did you get today? Is there a problem?
Homework after class: related exercises after the book.
Elementary Mathematics congruent triangles Courseware Part II
Congruent triangle
Theme: congruent triangles.
Teaching objectives:
1, knowledge target:
(1) Know what the corresponding elements of congruence, congruent triangles and congruent triangles are;
(2) Knowing the nature of congruent triangles, we can correctly use symbols to represent the congruence of two triangles;
(3) Can skillfully find out the corners and sides corresponding to two congruent triangles.
2, ability goal:
(1) Learn related concepts from the perspective of congruent triangles to improve students' ability to discriminate mathematical concepts;
(2) Cultivate students' ability to read pictures by finding out the corresponding elements of congruent triangles.
3, emotional goals:
(1) Stimulate students' spirit of loving science and being brave in exploration by feeling the corresponding beauty of congruent triangles;
(2) Get the feeling of mathematical knowledge through the development experience of autonomous learning, and cultivate students' creative skills of being brave in innovation and looking at problems in all directions.
Teaching emphasis: the nature of congruent triangles.
Difficulties in teaching: Finding the corresponding edges and angles of congruent triangles.
Teaching tools: ruler, microcomputer
Teaching method: self-study counseling.
Teaching process:
1, conformity and the introduction of congruent triangles's concept
(1) animation (geometric sketchpad) display:
Question: Can you find any wonderful relationship between these two triangles?
Ordinary students can find that these two triangles are completely coincident.
(2) Students do it themselves
Draw a triangle: the sides are 4cm, 5cm and 7cm respectively. Then stop talking. Two students at the same table cooperated and put two triangles together to overlap.
(3) Get the concept
Please describe in your own words:
Congruent triangles, corresponding vertex, corresponding angle and related mathematical symbols.
2, the discovery of the nature of congruent triangles:
(1) computer animation display:
Question: What is the relationship between the corresponding edge and the corresponding angle?
Students observe the animation and find that the three groups of edges corresponding to two triangles are equal and the three groups of angles corresponding to them are equal.
3. Finding corresponding edge, corresponding angle and application of congruent triangles property.
(1) Projection display theme:
d，AD∑BC，AD=BC
Analysis: Because the two triangles are completely coincident, the area and perimeter are equal. As for d, because AD and BC are corresponding edges, AD=BC. C meets the question.
Note: the key to solve this problem is to know that in two congruent triangles, the corresponding vertices are set in corresponding positions, and it is easy to find the wrong angle.
Analysis: The corresponding edge and the corresponding angle can only be found in two triangles, so they need to be separated from complex graphics.
Description: search by location element: there are equivalent elements, which are corresponding elements:
Then, according to the known corresponding elements, it is found that the opposite side of the corresponding angle of (1) congruent triangles is the corresponding edge, and the edge sandwiched by two corresponding angles is the corresponding edge; (2) The diagonal of the corresponding side of congruent triangles is the corresponding angle, and the angles of two corresponding side clips are the corresponding angles.
Description: use the "sports method" to find it.
Folding method: find two triangles whose center lines can overlap each other. After such folding, it is easy to find their corresponding elements.
Rotation method: When two triangles rotate around a certain point at a certain angle and can overlap, it is easy to find the corresponding elements.
Translation method: When two triangles are pushed along a straight line and can overlap, the corresponding elements can also be found.
Verification: AE∑CF
Analysis: prove the angle relationship (congruent angle, internal angle, etc. ) is usually used to prove the parallelism of straight lines. So I thought of the property of triangle congruence-the corresponding angles are equal.
∴AE∥CF
Note: the key to solve this problem is to find the corresponding angle accurately, and the translation method can be used.
Analysis: AB is not the corresponding edge of congruent triangles.
But it is converted into AB=CD and AB+CD=AD-BC through the corresponding edge.
It can be obtained by using known AD and BC.
Note: The key to solve this problem is to get the equality of the corresponding sides by using the congruence property of triangles.
(2) the solution of the problem
After these questions are given, students are required to think independently before answering them. Other students can supplement and improve them and put forward their own opinions. Teachers focus on guidance, teachers and students are the same. Summary: Several common methods to find corresponding edges and angles:
Projection display:
(1) The opposite side of the corresponding corner of congruent triangles is the corresponding edge, and the edge sandwiched by two corresponding corners is the corresponding edge;
(2) The diagonal of the corresponding side of congruent triangles is the corresponding angle, and the included angle of two corresponding sides is the corresponding angle;
(3) If there is a male party, the male party must be the corresponding party;
(4) If there is a common angle, it must be the corresponding angle;
(5) If there is an antipodal angle, the antipodal angle must be the corresponding angle;
The longest side (or angle) of two congruent triangles is the corresponding side (or angle), and the shortest side (or angle) is the corresponding side (or angle).
4. Practice independently in class to consolidate and improve.
This exercise is mainly to strengthen students' ability to read maps. At the same time, finding the corresponding edges and angles of congruent triangles is the key to learn geometry well in the future.
5. Summary:
(1) How to find the corresponding edges and angles of congruent triangles (basic method)
(2) The nature of congruent triangles
(3) Application of attributes
Let students express freely, other students supplement, systematize knowledge and construct it in their own way.
6. Homework
A. Written assignments P55#2, 3 and 4
B. Hand in homework (mid-term exam)
The third part of congruent triangles courseware for primary school mathematics
Teaching objectives
1, knowing what congruence is, the corresponding elements of congruent triangles and congruent triangles;
2. Symbols can be used to correctly represent the congruences of two triangles;
3, can skillfully find out the corresponding vertices, corresponding edges and corresponding angles of two congruent triangles;
4. Understanding the nature of congruent triangles and using it to solve simple problems requires students to determine the corresponding elements of congruent triangles and their understanding of the nature of congruent triangles;
5. Stimulate the spirit of loving science and being brave in exploration by feeling the beauty corresponding to congruent triangles. Through text reading and graphic reading, we can construct mathematical knowledge, experience the process of acquiring mathematical knowledge, and cultivate students' creative skills of being brave in innovation and examining problems from all directions.
[answer]
Explore the essence of congruent triangles.
[difficulties]
Solving simple problems with congruent triangles's nature requires students to determine the corresponding elements of congruent triangles and their understanding of congruent triangles's nature.
Teaching process arrangement
Activity 1 Observe graphics by computer projection and explore the concept of congruent graphics.
Activity 2 Observe the translation, folding and rotation of two graphs.
Activity 3 Conformal Exercise
Activity 4 Observe the changes of two translated triangles (courseware demonstration), and cut out two congruent triangles by hand.
Activity 5 Explore the essence of congruent triangles.
(Courseware demonstration)
Activity 6 Application of congruent triangles Nature
Activity 7 Summarize and assign homework.
Observe and find the graphics with the same shape and size in life, and get conformal experience.
Using two figures with the same shape and size, the concept of congruence is obtained through translation, folding and rotation experiments.
Consolidate the concept of congruence
By translating two triangles with the same shape and size
And compared with myself, the concept of conformal triangle is obtained.
Through the transformation of graphics, the corresponding concepts are formed and the properties of conformal triangles are obtained.
Solving problems by using congruent triangles's properties
Looking back, we can further understand and grasp the concept of congruent triangles and the nature of congruent triangles.
Teaching process design
Problems and scenarios
Teacher-student behavior
Design intent
Activity 1
(1) Observe the following patterns (the patterns displayed by the computer are different from the textbooks). Do the students point out whether these patterns are the same shape and size?
(2) Can you give some practical examples from your life?
(3) According to the requirements of the textbook, put a triangular template on the cardboard, draw a figure, and cut the cardboard according to the figure. Observe whether the shapes and sizes of the cut cardboard are exactly the same and whether they are completely coincident.
Teachers demonstrate courseware, ask questions, and students think and communicate.
Students think and express their views.
Students cite examples from life, and teachers praise and encourage creative examples.
The teacher gave the concept of congruence.
Teachers ask questions, students operate, observe and answer questions.
In this activity, teachers should focus on:
( 1)
Students' ability to observe and discover conformality, whether the cited ions are limited in a certain range and whether they are innovative;
(2) Whether the students can cut the cardboard according to the requirements, overlap the cardboard accurately, and observe carefully.
Stimulate students' interest in inquiry with a model close to students' life.
Through the question (1), guide students to observe the graph from the angle of its shape and size.
Graphics are conformal and exist in a large number in life, so create such problem situations, guide students to pay attention intentionally, and stimulate students to think and associate actively; Guide students to further contact with life and stimulate their desire to explore.
Through hands-on practice, you can get a conformal experience.
[Activity 2]
Observe whether the shapes and sizes of the following figures have changed before and after translation, folding and rotation.
The teacher made a request.
Students realize that the position of the figure has changed, but it is still congruent after translation, folding and rotation.
Cultivate students' ability to recognize graphics.
[Activity 3]
Practice of conformal knowledge.
The teacher asked questions.
Students think and answer questions.
Students can find the answer accurately and quickly.
Use the concept of congruence
[Activity ]4
question
Hands-on operation, put the cut two triangular cardboard in the picture.
△
ABC's seat, try it:
Such as: textbook map 13. 1, map 13.2,
Figure 13.3
Observe whether △ABC changes in translation, folding and rotation. Are the two triangles in the picture the same?
The teacher made a request.
Students practice with two triangular pieces of cardboard.
The teacher showed it with courseware.
Students guess and express their opinions to get the concept of congruent triangles.
Teachers should pay attention to:
( 1)
Understanding of practical operation.
(2)
Can you understand the position change of triangle, but after translation, folding and rotation, the two figures are still congruent.
Students practice analysis, summarize the essence of graphic transformation and deepen their understanding of graphic transformation.
[Activity ]5
question
Courseware demonstration:
( 1)
Overlap two triangles completely, observe and point out the overlapping vertices, edges and angles.
(2)
How to express the congruence of two triangles with mathematical symbols?
(3)
Look at two triangles and find the corresponding sides and angles.
(4) Observe the relationship between the corresponding edges and angles of two overlapping triangles.
The teacher demonstrated the courseware and asked questions.
Students practice communication and draw conclusions.
The teacher gives the concepts of corresponding vertex, corresponding edge and corresponding angle and writes them on the blackboard.
Students observe and answer questions. The teacher guides the students to summarize the nature of the triangle and write it on the blackboard.
Teachers should pay attention to:
( 1)
Understanding the concepts of corresponding vertex, corresponding edge and corresponding angle.
(2)
Writing of congruent symbols.
(3)
Understanding of the nature of congruent triangles.
In the process of demonstrating courseware by teachers, students establish corresponding concepts.
Students learn to master the expression of congruent triangles and the use of congruent symbols.
Students master the nature of congruent triangles.
[Activity ]6
( 1)
Courseware demonstration questions:
Fill in: (as shown below)
(2)
Exercise:
As shown, it is known that Δ δOCA?δOBD,
Please name their corresponding edges and angles.
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(3) Broaden the exploration:
As shown in the figure below, the rectangular ABCD is folded along AM, so that point D falls on point N on BC. If AD = 7cm, DM = 5cm, ∠ DAM = 39, then an = _ _ cm, nm = _ _ cm, ∠ NAB = _ _.
The teacher asked questions.
Students explore in groups.
Observe whether students can quickly find the corresponding edges and corners.
The teacher demonstrated the problem with courseware.
Students' mastery of the corresponding edges and corners again.
The teacher asked questions.
Students think independently, answer and tell the process of solving problems.
The teacher gave the answer to the question.
In this activity, teachers focus on:
( 1)
Can students find the corresponding edges and corners quickly and accurately?
(2)
Students' understanding of congruent triangles's essence.
(3)
The degree of communication and activity participation between classmates.
Students master how to find the corresponding edges and angles.
Further cultivate students' ability to recognize figures and deepen their understanding and mastery of the nature of congruent triangles.
Explore more complex graphics by using the nature of congruent triangles, and initially cultivate students' ability to comprehensively use the nature of congruent triangles.
[Activity ]7
( 1)
Summary: talk about the harvest of this activity.
(2)
Assign homework after class
Exercise on page 92 of the textbook 1.
Students summarize in groups.
Teachers assign homework, and students finish it independently after class.
In this activity, teachers should focus on:
( 1)
The habit of combing and summarizing knowledge.
(2)
Consciousness of group cooperation
(3)
Students' understanding of this section.
(4)
Students' emotional understanding of congruent triangles.
Deepen students' understanding of knowledge and promote students' reflection on the classroom.
Consolidate, improve and reflect. Let students master knowledge.
1. Prepare seven pieces of square colored paper with different colors, fold one of them in half, and draw the cross section of half a ho