Lesson Plan | Technical Methodology | Triangles: Congruence

Objectives

Duration: 10 - 15 minutes

This stage of the lesson plan aims to prepare students to clearly and objectively understand the concept of congruent triangles and the main cases of congruence. By focusing on the development of practical skills, the lesson not only provides a solid theoretical understanding but also prepares students to face real problems that may arise in professional contexts. This ensures that the knowledge acquired is applicable and relevant to the job market.

Main Objectives

1. Understand that two congruent triangles are those that have their angles and sides equal to each other.

2. Know and identify the main cases of triangle congruence (Side-Side-Side, Side-Angle-Side, Angle-Side-Angle, Angle-Angle-Side, and Hypotenuse-Leg).

3. Apply the cases of congruence to solve practical problems, simulating situations in the job market that involve the use of congruent triangles.

Side Objectives

1. Develop teamwork and effective communication skills when discussing and solving problems in a group.
2. Encourage critical thinking and analytical ability by evaluating different methods to verify the congruence of triangles.

Introduction

Duration: 10 - 15 minutes

The purpose of this stage is to introduce the topic in an engaging way and show the practical relevance of congruent triangles in the job market. By contextualizing the subject and presenting curiosities, the aim is to spark students' interest and prepare them for the practical activities that will be carried out throughout the lesson.

Contextualization

Understanding triangles and their properties is a fundamental skill in various fields of knowledge and the job market. From civil construction to mechanical engineering, triangle congruence is used to ensure the precision and stability of structures. The ability to identify and apply the cases of congruence is essential for solving complex problems and creating innovative solutions.

Curiosities and Market Connection

Did you know that civil engineers use triangle congruence to ensure that bridges and buildings are constructed accurately? Additionally, in the technology field, graphic designers utilize concepts of congruence to create shapes and symmetrical patterns that are visually appealing and functional in user interfaces. Triangle congruence is also used in manufacturing processes and the assembly of parts in the automotive industry, where precision is crucial for the safety and efficiency of vehicles.

Initial Activity

Ask the students: How do you think triangles are used in the construction of bridges and buildings? Show a short video (2-3 minutes) demonstrating the application of triangles in civil engineering, highlighting how congruence is used to ensure the stability of structures.

Development

Duration: 70 - 75 minutes

The purpose of this stage is to consolidate the students' understanding of the concepts of triangle congruence through practical activities and reflections. By working in groups, students develop collaboration and communication skills, and by facing mini challenges, they apply the knowledge acquired in real situations, preparing for professional contexts.

Covered Topics

1. Definition of congruent triangles
2. Cases of triangle congruence (SSS, SAS, ASA, AAS, HL)
3. Application of the cases of congruence in practical problems

Reflections on the Theme

Guide students to reflect on how triangle congruence can be useful in everyday and professional situations. Ask the students: How can precision in triangle congruence impact the construction of safe and efficient structures? Encourage them to think of examples beyond civil engineering, such as in industrial part manufacturing and graphic design.

Mini Challenge

Building a Stick Bridge

Students will build a mini bridge using popsicle sticks and hot glue, applying the concepts of congruent triangles to ensure the stability of the structure.

Instructions

1. Divide students into groups of 4-5 members.
2. Distribute popsicle sticks and hot glue tubes to each group.
3. Explain that they must build a bridge based on congruent triangles, ensuring that all triangles used in the structure are congruent.
4. Set a time limit of 30 minutes for building the bridge.
5. At the end of the time, each group must present their bridge and explain how they applied the concepts of congruence in the construction.
6. Conduct a strength test by placing weights gradually on the bridges to check for stability.

Objective: Apply the concepts of congruent triangles in a practical construction activity, reinforcing the importance of precision and stability in structures.

Duration: 40 - 45 minutes

Evaluation Exercises

1. Ask the students to solve the following problems in groups:

Determine if triangles ABC and DEF are congruent, given the following measures: AB = DE, BC = EF, and angle B = angle E. Given a triangle with sides of 5 cm, 7 cm, and 10 cm, and another triangle with sides of 5 cm, 7 cm, and 10 cm, prove that the two triangles are congruent by the SSS case. In a graphic design project, two triangles need to be congruent to create a symmetrical pattern. What measures and angles do you need to check to ensure that they are congruent?

2. After solving the problems, discuss the answers with the class, encouraging students to share their strategies and reasoning.

Conclusion

Duration: (15 - 20 minutes)

The purpose of this stage is to consolidate learning, reinforcing the theoretical and practical concepts covered in the lesson. By promoting reflection on the activities carried out and their applications, students are encouraged to recognize the value of the knowledge acquired and the importance of its application in real and professional contexts.

Discussion

Encourage a discussion among students about the activities carried out during the lesson. Ask what they found most challenging when building the stick bridges and how they applied the concepts of triangle congruence. Foster reflection on the importance of precision in building structures and how these skills can be useful in their future careers. Ask students to share examples of everyday or professional situations where triangle congruence can be applied.

Summary

Summarize the main content presented: the definition of congruent triangles, the cases of congruence (SSS, SAS, ASA, AAS, HL), and the application of these concepts in practical problems. Reinforce the understanding that two triangles are congruent if they have equal angles and sides. Highlight the importance of practice and precision in solving problems involving triangles.

Closing

Explain how the lesson connected theory to practice through the building of stick bridges. Emphasize the relevance of these skills in the job market, especially in areas like engineering, architecture, graphic design, and manufacturing. Stress the importance of continuous learning and the practical application of acquired knowledge to solve real problems.