Contextualization

Triangles are elementary geometric figures, and their study is fundamental to mathematics and its practical applications. The concept that encompasses triangles is one of the first to be introduced when we begin to study geometry. Triangles are figures formed by three sides and three angles. The classification of triangles can be done in two ways: according to the measure of the sides and according to the measure of the angles. In this project, we will focus on angular classification.

Triangles can be classified into right triangles, acute triangles and obtuse triangles. The right triangle has a right angle, that is, an angle of 90 degrees. The acute triangle has all its acute angles, that is, all its angles are less than 90 degrees. Finally, the obtuse triangle has an obtuse angle, that is, an angle greater than 90 degrees.

A curious fact is that the sum of the angles of a triangle is always equal to 180 degrees, regardless of the individual measure of each angle. This means that any triangle, be it right, acute or obtuse, will have the sum of its angles equal to 180 degrees. This is a very important and useful feature for solving many mathematical problems.

Importance of Triangles

Triangles have fundamental importance in several areas of knowledge, from engineering and architecture to navigation, astronomy and art. For example, in engineering and architecture, triangles are used to create strong and stable structures. In navigation and astronomy, triangles are used to calculate distances and positions. In art, triangles are used to create visually pleasing shapes and patterns.

In addition, the study of triangles is also essential for understanding more advanced concepts in mathematics, such as calculus and trigonometry. For example, the Pythagorean Theorem, one of the most famous theorems in mathematics, is based on the properties of right triangles.

Practical Activity

Activity Title: The World of Triangles

Project Objective

The project "The World of Triangles" aims to meet two main objectives:

1. To apply the concept of angular classification of triangles in a practical and playful way, aiming to fix this theoretical knowledge and broaden the understanding of this content.

2. To stimulate socio-emotional skills such as teamwork, time management, critical thinking and communication.

Detailed project description

The students will be divided into groups of 3 to 5 people. They will be challenged to build a mural with all the different possibilities of classifying triangles according to the measure of the angles. This should be done using stationery and include a brief written description of each type of triangle.

The groups must research the topic, collect materials, create a project for the mural and finally build it. During the process, they must record and document everything for the preparation of the final report.

The estimated time for the activity is 2 to 4 hours per student over a week, which includes both the creation of the mural and the preparation of the report.

Required materials

• Cardstock or cardboard for the base of the mural;
• Paper of different colors to create the triangles;
• Felt-tip pen or marker;
• Ruler;
• Scissors;
• Glue.

Step-by-step guide to carrying out the activity

1. Research and review the concept of triangle classification based on angles. Use the resources provided and seek other sources if necessary.

2. Create a sketch of the mural with the representation and classification of the triangles. This can be done on paper or digitally.

3. Using colored paper, cut out the triangles according to the angular classification.

4. Attach the triangles to the mural and label each triangle with its classification and a brief description of the properties related to its angles.

5. Document the entire process, taking pictures of the mural at different stages of creation and recording the decisions made by the group and the challenges encountered.

6. Write the final report, including the sections of introduction, development, conclusions and bibliography.

Project Deliverables

Each group must submit the final mural and a report that must include:

1. Introduction: Description of the importance of triangles and contextualization of the project, including how the project connects to the concept of angular classification of triangles

2. Development: Detailed description of the steps taken to make the mural, explanation of the theory behind the classification of triangles based on angles, and a presentation and discussion of the results.

3. Conclusion: Recap of the main points, lessons learned from the project and reflection on the challenges encountered and how they were overcome.

4. Bibliography: References of the resources used in the project for research and learning.

Students should make sure that the report is well-written and clear, so that anyone reading it can understand what was done and why it was done, as well as see the applicability of triangle classification in the real world.