Objectives (5 - 7 minutes)

1. Understanding the concept of triangle congruence - The teacher must ensure that students understand what it means for two or more triangles to be congruent. This includes understanding the congruence criteria.

2. Applying the criteria for triangle congruence - Students should be able to apply the learned congruence criteria to determine if two triangles are congruent or not. This requires them to be able to identify and use relevant information, such as angle and side measurements.

3. Solving problems of triangle congruence - Students should be able to solve problems involving triangle congruence. This includes applying the congruence criteria to determine if the given triangles are congruent and, if so, to find the measurements of unknown angles or sides.

Secondary Objectives:

• Develop logical and analytical thinking - Through solving problems of triangle congruence, students should be able to develop their logical and analytical thinking skills.

• Promote interaction and collaboration in the classroom - The teacher should encourage discussion and collaboration among students during the lesson, thus promoting the development of communication and collaboration skills.

Introduction (10 - 15 minutes)

1. Review of previous concepts (3 - 5 minutes) - The teacher should start the lesson by reviewing the geometry concepts that are fundamental to understanding triangle congruence. This includes the definition of a triangle, types of triangles (equilateral, isosceles, scalene), triangle properties (sum of internal angles, triangle inequality).

2. Problem situations (3 - 5 minutes) - The teacher should present two problem situations involving triangle congruence. One may involve determining the congruence of two triangles, and the other may involve solving an application problem that requires the use of congruence criteria.

   • Example of problem situation 1: "If two triangles have congruent sides of 5 cm, 6 cm, and 7 cm, are they congruent?"
   • Example of problem situation 2: "A right triangle with a hypotenuse of 10 cm and an acute angle of 30 degrees is congruent to a right triangle with a hypotenuse of 5 cm and an acute angle of 60 degrees?"

3. Contextualization (2 - 3 minutes) - The teacher should explain the importance of triangle congruence, showing how it is applied in different areas such as architecture, engineering, game design, computer graphics, among others.

4. Introduction to the topic (2 - 3 minutes) - To spark students' interest, the teacher can share some curiosities about triangle congruence.

   • Curiosity 1: "Did you know that triangle congruence is one of the first things architects and engineers learn? This is because triangle congruence allows them to design structures that are safe and stable."
   • Curiosity 2: "Did you know that triangle congruence is one of the main tools used in computer graphics to create realistic 3D images? This happens because when triangles in a mesh are congruent, the resulting surface looks smooth and uniform."

With this Introduction, students should be prepared to start the lesson on triangle congruence.

Development (20 - 25 minutes)

1. Theory Presentation (10 - 12 minutes)

   • Definition of Triangle Congruence (2 - 3 minutes) - The teacher should start by defining what it means for two triangles to be congruent. It should be emphasized that triangle congruence implies that they have the same angles and corresponding equal sides.

   • Congruence Criteria (3 - 5 minutes) - The teacher should present the congruence criteria, which are the conditions that must be met for two triangles to be congruent. The congruence criteria are: SSS (Side-Side-Side), SAS (Side-Angle-Side), ASA (Angle-Side-Angle), AAS (Angle-Angle-Side), and HL (Hypotenuse-Leg). The teacher should explain each of these criteria, using examples and diagrams to illustrate.

   • Application of Congruence Criteria (2 - 3 minutes) - The teacher should explain how to apply the congruence criteria to determine if two triangles are congruent or not. It should be emphasized that, to apply the congruence criteria, it is important to identify and compare the corresponding sides and angles of the triangles.

   • Theorems of Triangle Congruence (2 - 3 minutes) - The teacher should present the theorems that follow from the congruence criteria. These theorems include the Pythagorean Theorem, the Isosceles Triangle Theorem, and the Equilateral Triangle Theorem. The teacher should explain each of these theorems, using examples and diagrams to illustrate.

2. Practical Activities (10 - 13 minutes)

   • Activity 1: Solving Problems of Triangle Congruence (5 - 7 minutes) - The teacher should provide students with a series of problems involving triangle congruence. Students should work in pairs or groups to solve the problems. The teacher should circulate around the room, providing guidance and clarifying doubts.

   • Activity 2: Building Congruent Triangles (5 - 6 minutes) - The teacher should provide students with a series of line segments and a set of protractors and compasses. Students should work in pairs or groups to build congruent triangles. The teacher should circulate around the room, providing guidance and clarifying doubts.

   • Discussion and Correction (2 - 3 minutes) - After the conclusion of the activities, the teacher should promote a classroom discussion for students to share their solutions and conclusions. The teacher should then correct any errors and clarify any remaining doubts.

This Development should allow students to gain a solid understanding of the concept of triangle congruence and become proficient in applying the congruence criteria.

Return (8 - 10 minutes)

1. Group Discussion (3 - 4 minutes) - The teacher should promote a group discussion with all students. Each group should share the solutions or conclusions they found during the practical activities. The teacher should encourage students to explain the reasoning behind their solutions, highlighting the importance of thinking analytically and applying the congruence criteria correctly.

2. Connection with Theory (2 - 3 minutes) - After the group discussion, the teacher should make the connection between the practical activities and the theory presented. It should be emphasized how the application of the congruence criteria allowed students to determine the congruence of triangles and solve the proposed problems. The teacher can highlight specific examples of how the congruence criteria were applied in the practical activities.

3. Individual Reflection (2 - 3 minutes) - The teacher should propose that students reflect individually on what they learned in the lesson. For this, the teacher can ask the following questions:

   1. "What was the most important concept you learned today?"
   2. "What questions have not been answered yet?"

   Students should have a minute to think about these questions. The teacher can then ask some students to share their answers, allowing other students to learn from their peers' reflections.

4. Feedback and Closure (1 minute) - Finally, the teacher should thank the students for their participation and effort during the lesson. The teacher can provide general feedback on the class performance and encourage students to continue practicing the concepts and skills learned. The teacher should then announce the topic of the next lesson, thus creating a connection between topics and encouraging continued learning.

With this Return, students will have the opportunity to consolidate their learning, reflect on what was learned, and identify any remaining doubts they may have. Additionally, the teacher will be able to assess the effectiveness of the lesson and plan any necessary adjustments or revisions for future lessons.

Conclusion (5 - 7 minutes)

1. Summary of Contents (2 - 3 minutes) - The teacher should give a brief summary of the main points covered during the lesson. This includes the definition of triangle congruence, the congruence criteria, the application of criteria to determine triangle congruence, and the theorems that follow from the criteria.

2. Connection between Theory and Practice (1 - 2 minutes) - The teacher should explain how the lesson connected theory (the definition, criteria, and theorems) with practice (the problem-solving and triangle construction activities). It should be emphasized how the application of the congruence criteria allowed students to determine triangle congruence and solve practical problems.

3. Suggestion of Additional Materials (1 - 2 minutes) - The teacher should suggest some extra materials for students to deepen their knowledge of triangle congruence. This may include math books, educational websites, explanatory videos, online math games, among others. The teacher should emphasize that these materials are optional but can be useful for students who wish to review the content or explore related topics in more depth.

4. Importance of the Topic (1 minute) - Finally, the teacher should summarize the importance of the topic addressed for everyday life. It can be highlighted how triangle congruence is used in various areas such as architecture, engineering, game design, computer graphics, among others. The teacher can also reinforce the importance of developing logical and analytical thinking skills, which are essential not only for mathematics but also for many other areas of life.

With this Conclusion, students should have a clear and comprehensive understanding of the lesson topic, as well as a sense of its relevance and application. Additionally, they will have additional resources to continue learning and exploring the subject on their own.