Contextualization

Theoretical Introduction

Triangles are polygons formed by three sides, three vertices, and three internal angles. They are a fundamental figure in geometry, as they are the basis for the formation of all other flat figures. Triangles can be classified in various ways, but in this project, we will focus on the classification based on the sides.

Triangles can be classified as equilateral, isosceles, and scalene based on the lengths of their sides. A triangle is called equilateral when all its sides have equal lengths. An isosceles triangle, on the other hand, has at least two sides with equal lengths. Finally, a scalene triangle is one in which all sides have different lengths.

Furthermore, it is worth noting the importance of the theorems associated with these figures, such as the Pythagorean Theorem, which relates the sides of a right triangle, and the conditions for a set of segments to form a triangle.

Contextualization of the Theme

Although at first glance, the study of triangles may seem purely academic, it has several practical applications. In architecture and engineering, for example, the stability of structures often depends on the use of triangles in their construction. In the field of navigation, triangles are also very useful, as pilots and navigators can use the properties of these figures to determine distances and directions.

Additionally, knowledge about triangles helps us understand natural phenomena and more complex mathematical constructions. They are the basis for trigonometry, a field of mathematics that studies the relationships between the sides and angles of triangles and has numerous applications in sciences such as physics, engineering, astronomy, among others.

Practical Activity

Activity Title: 'Modeling and Discovering - Triangles'

Project Objective

The purpose of this activity is to allow students to explore the classification of triangles based on their sides and discover their properties through observation, measurement, and group discussion.

Detailed Project Description

Students will be divided into groups of 3 to 5 people and will have one month to complete the project. Each group will be tasked with creating different models of triangles (equilateral, isosceles, and scalene) using different materials and then categorizing them according to the number of equal sides they have. They will also be encouraged to explore the properties of triangles, such as the internal angles and the relationships between the sides.

Required Materials

• Colored cardboard paper
• Ruler
• Compass
• Scissors
• Pencil
• Pen
• Glue

Detailed Step-by-Step

1. Each group must choose three different colors of cardboard paper, one to represent each type of triangle.
2. Using the ruler and compass, students will draw and cut out several instances of each type of triangle on the corresponding colored cardboard paper. The triangles should have different sizes, but each set of triangles (equilateral, isosceles, and scalene) should have the same measurements among themselves.
3. Next, students will categorize the triangles according to the number of equal sides they have and identify each one by writing the type on the back of the cardboard.
4. Then, the groups will have a review session: they will mix all the triangles and then try to classify them correctly.
5. With the triangles still grouped, students will discuss the properties of the triangles. They will measure the sides and internal angles of the triangles to verify, for example, if the internal angles add up to 180° and if the perceived relationships hold for the various sizes of triangles.
6. Once the practical steps are completed, the group will work on the project report. This report should contain four main sections: Introduction, Development, Conclusions, and Bibliography.

Project Delivery and Report Writing

The project delivery will consist of the set of triangles produced and a complete report detailing the process and conclusions drawn. The report should follow the following format:

1. Introduction: Should contain the study objective, the motivation for the work, and the relevance of triangles in everyday life and in various areas of knowledge.

2. Development: Should contain a theoretical discussion on the definition and properties of triangles, as well as a detailed description of how the practical activity was carried out. Here, the student should describe all the project steps, from the choice of materials to the completion of the activity. Additionally, the student should also explain the methodology used for the classification and study of triangles, and present and discuss the results obtained.

3. Conclusions: Should include a summary of the findings, what was learned during the activity, and the conclusions drawn from the project. Additionally, students are encouraged to discuss the difficulties and challenges encountered during the project and how they overcame these obstacles.

4. Bibliography: The last section should list all references consulted for the work, such as books, websites, videos, among others.