Context

Geometry is one of the branches of mathematics that we come into contact with since childhood, even before learning to count. It is what allows us to understand the space around us, the shapes, and their properties. Triangles are one of these shapes and we can find them everywhere: on the play button keys, at the top of a mountain, in the way some streets intersect, and even in the love triangles of soap operas!

That being said, understanding the properties of triangles is fundamental. This unique geometric figure has incredible importance in various areas such as architecture, engineering, art, video game programming, and much more. Knowing this, you may wonder, how can studying triangles be a path to better understand the world around us?

To understand the importance of studying triangles, let's look at history. In ancient Egypt, for example, triangles were used in the construction of pyramids. Calculation and measurement techniques based on the geometry of triangles allowed these giant structures to be erected with precision. In Ancient Greece, mathematicians developed a series of theorems related to triangles whose applications can be seen in physics, astronomy, engineering, among other areas.

In this project, we will focus on the classification of triangles according to their sides, a fundamental concept in geometry. Specifically, we will study equilateral triangles (all sides are equal), isosceles triangles (two sides are equal), and scalene triangles (no sides are equal). Recognizing their importance, you will have the opportunity to develop practical and theoretical activities that will solidify the acquired knowledge. With the help of visual and interactive resources, you will be able to explore the properties of these triangles in a playful and engaging way.

For further study and support, we recommend the use of the following resources:

• Khan Academy: Triangles - An excellent learning platform that offers video lessons and practical exercises on a variety of topics.
• Mathway: Triangle Classification - On this page, you will find a detailed explanation of triangle classification.
• YouTube: Matemática Rio Channel - This channel offers educational videos on a variety of math topics, including triangles.

Practical Activity

Activity Title: Exploring Triangles: A Study on their Classifications

Project Objective:

Explore the properties of triangles (equilateral, isosceles, and scalene) through practical activities. Students will build triangle models and discuss their characteristics, thus enhancing their understanding of said triangles and their properties.

Detailed Project Description:

Groups will carry out a series of practical activities associated with the construction and analysis of triangles. The project will consist of two phases: in the first phase, students will build triangle models, and in the second phase, they will conduct an investigation on the properties of these triangles.

Required Materials:

1. Colored cardboard paper (to build the triangle models)
2. Ruler
3. Scissors
4. Pencils and colored pens
5. Tape or glue

Detailed Step-by-Step Guide for the Activity:

Phase 1: Construction of triangle models

1. Groups should divide into three subgroups, each responsible for building a type of triangle (equilateral, isosceles, and scalene).
2. Each subgroup should measure and cut three line segments, each representing a side of the respective triangle.
3. Next, they should join the segments using tape or glue to form a triangle.
4. Finally, each subgroup should present their model to the rest of the group, explaining the characteristics of the constructed triangle.

Phase 2: Investigation of triangle properties

1. After construction, groups should research the properties of the triangles they built (equilateral, isosceles, scalene).
2. Each group should discuss and record the similarities and differences between the three types of triangles.
3. The group should also formulate questions about the properties of triangles and try to answer them based on the research.
4. At the end of this stage, the groups should be able to classify a given triangle based on its properties.

The entire activity should be completed within a period of two to four hours, and students should record all steps taken and observations made during the activity.

Project Submission:

After the practical part of the project, each group must produce a detailed report that includes the following topics:

• Introduction: In this part, the group should contextualize the study of triangles, their relevance and application in the real world, and the project's objective.
• Development: The group should present the theory about the studied triangles, explain in detail the activities carried out, the methodology used, the results obtained, and the discussion about them.
• Conclusion: The group should conclude the work by summarizing its main points, explaining the learnings obtained, and the conclusions drawn from the project.
• Bibliography: The group should indicate the sources they relied on to work on the project such as books, web pages, videos, etc.

This report must be submitted within a week after the practical activity. This document is very important to understand what each group understood about the classification of triangles and the properties that each type of triangle possesses. Therefore, each group should strive to be clear, concise, and comprehensive in their explanations and discussions.