Contextualization

Triangles are figures known to all of us who have had any contact with basic geometry. They are simple figures, made of only three straight lines, but they hide an impressive mathematical complexity and have numerous practical applications in the real world.

In mathematics, a triangle is defined as a flat geometric figure formed by three line segments that intersect at three non-collinear points. The points of intersection are called the vertices of the triangle, while the line segments are its sides.

Triangles can be classified in several ways, but the most common are by the length of their sides and by their angles. As far as sides are concerned, we have the equilateral triangle (all sides equal), the isosceles (two equal sides) and the scalene (all sides different). In terms of angles, we have the acute triangle (all angles less than 90°), the rectangle (with one angle of 90°) and the obtuse (with one angle greater than 90°).

These are just the most basic classifications of triangles, but there are many others that explore more complex properties of these figures.

In the real world, triangles are ubiquitous and essential to our daily lives. They are the fundamental building block of many structures, from the way we put tiles on a roof to the design of bridges and towers. In addition, they are used in various disciplines, such as physics, engineering, arts, architecture and, of course, mathematics.

The knowledge of triangles and their properties is also crucial in activities such as navigation, where trigonometry (a branch of mathematics that studies triangles) is used to locate the position of a ship or plane. Understanding triangles and their properties is therefore a practical and applied skill.

To deepen your knowledge on the subject, we recommend the following resources in Portuguese:

1. Só Matemática - Triângulos: Website with detailed lessons on triangles, their properties and classifications.
2. Manual do Mundo - Origami de Triângulo: Video that teaches you how to make a triangle origami, which can help you better understand the shape and properties of these figures.
3. Khan Academy - Triângulos: Online educational platform with interactive lessons on triangles and geometry in general.

Practical Activity: "Exploring the World of Triangles"

Title of the activity: "Creating Triangle Models and Practical Application"

Objective of the project:

The objective of this project is to explore in depth the concept and properties of triangles, applying theoretical knowledge in the creation of three-dimensional models and in a practical activity related to architecture and civil engineering.

Detailed description of the project:

In this project, students will first conduct thorough research on the types of triangles and their properties, using the recommended resources and others they deem relevant. Then, they must build three-dimensional models of the different types of triangles, exploring their properties. Finally, as a practical application activity, students must design and build a structure, such as a bridge or a tower, using triangles as their main structural element.

Materials needed:

• Cardstock
• Glue
• Scissors
• Colored pens
• Pencil
• Ruler
• Recyclable materials for building the structure (such as popsicle sticks, straws, bottle caps, etc.)

Detailed step-by-step to carry out the activity:

1. Theoretical research: students will research the types of triangles (scalene, isosceles, equilateral, acute, rectangular and obtuse) and their properties. This research should be consolidated in a document that will be part of the final report.
2. Model creation: using cardstock, glue, scissors and colored pens, students should create three-dimensional models of different types of triangles, in order to explore their properties in practice.
3. Design of a structure: students will design a structure (a bridge or a tower, for example), which should be predominantly composed of triangles. This design should include a drawing of the structure and an explanation of how the triangles are used and why they were chosen.
4. Construction of the structure: use of recyclable materials to build the projected structure.
5. Writing the final report: students shall write a report, in which they shall contextualize the work, present the theoretical research, explain the methodology used in the construction of the models and the structure, and discuss the results obtained. The report should also contain the bibliography used.

Project deliverables and suggested activities:

The project will be assessed in two main parts: the practical part, which includes the models of triangles and the built structure, and the written part, which consists of the final report. Creativity, teamwork, quality of research, execution of the creation of models and structure and quality of the written report will be taken into account for the evaluation.

For the final report, students should follow the following structure:

1. Introduction: students should contextualize the work, present the objective of the project and explain the relevance of triangles and their properties in everyday life.
2. Development: students should present the theoretical research on triangles, explain the methodology used in creating the models and the structure and present and discuss the results obtained.
3. Conclusion: students must resume the main points of the project, explain the learning and conclusions about the practical application of triangles.
4. Bibliography: students shall indicate the sources used during the research and elaboration of the project.