Contextualization

Mathematics is a powerful tool that helps us understand the world around us. It has practical applications in various areas, from physics to arts and design. One of the most fundamental areas of mathematics is Geometry, in which the study of figures and shapes is a crucial component. In the field of geometry, the concept of congruent triangles is a fundamental tool that allows mathematicians and us to understand and solve complex problems.

Congruent triangles are triangles that have the same size and shape, meaning their corresponding sides and corresponding angles are equal. This means that if you move, rotate, or mirror a congruent triangle, it will fit perfectly onto the other. Triangle congruence is an essential part of geometry and has a multitude of applications.

Importance of the Theme

Triangle congruence plays an important role in various disciplines and real-life contexts. From GPS navigation calculations to determining the distance between stars in astrophysics, from deducing mathematical theorems to creating designs and patterns in arts and architecture. Understanding triangle congruence opens a window to a deeper understanding of the reality around us.

Furthermore, triangle congruence is one of the foundations of the study of geometry and a crucial step in the mathematical disciplines that you, as high school students, will face. Therefore, it is important not only to learn about triangle congruence but also to understand how to apply it to solve problems and concrete situations.

Practical Activity

Activity Title: "The Art of Triangle Congruence"

Project Objective

This project aims to apply and explore the concept of triangle congruence in a practical and playful way, through the creation of geometric art. Students will have to apply their knowledge of triangle congruence to create a design mural using only congruent triangles.

Detailed Project Description

The project will be carried out by groups of 3 to 5 students. The group will have to create a geometric art mural using colored paper, glue, and scissors. The mural must be entirely made of congruent triangles, meaning triangles with the same angles and side lengths. The group has total creative freedom to choose the colors, patterns, and final shape of the mural, as long as all triangles used are congruent.

Required Materials

• Colored paper
• Ruler
• Pencil
• Scissors
• Glue

Step by Step

1. Gather your group and start planning your mural. Decide on the colors you will use, the arrangement of the triangles, and the overall design. Remember that all triangles used must be congruent.
2. Once the design is decided, start drawing the triangles on the colored paper. Use the ruler to ensure all sides and angles are equal. Each group member should participate in this step.
3. Cut out the drawn triangles using the scissors.
4. Begin gluing the triangles onto the mural base according to the planned design. Make sure all glued triangles are congruent.
5. Upon finishing the mural, critically analyze the work, checking if the objective was achieved and discussing what was learned during the process.
6. Document all project steps and write a report, as described below.

Project Deliverables

In addition to the geometric art mural, the group must deliver a detailed report on the project. The report should be in the format of a scientific article and include the following sections:

1. Introduction: Provide context for the theme of triangle congruence and discuss its relevance. Clearly state the project's objective and briefly describe the activity carried out.

2. Development: Explain in detail the theory of triangle congruence. Document the project's step by step, discussing the decisions made during the mural construction. Discuss the difficulties encountered and how they were resolved. Present images of the mural and discuss the relationship between the mural and the theory of triangle congruence.

3. Conclusion: Summarize the main points of the work, discussing what was learned during the project. Talk about the importance of teamwork and the skills developed. Recap the concept of triangle congruence and how the mural demonstrates this concept.

4. Bibliography: List all reference materials the group used to understand the theory and to build the mural. This may include textbooks, websites, YouTube videos, and more.

This project should help you understand triangle congruence more clearly while developing important skills such as teamwork, time management, problem-solving, and creative thinking.