Context

Theoretical Introduction

Triangles are polygons with three sides and, as such, are fundamental in basic geometry. Their properties allow for a variety of applications in solving real and theoretical problems. Understanding the relationship between the sides of a triangle is vital to comprehend many of the principles that govern the world around us.

The elements that compose triangles - such as the sides, the internal angles, and the types of triangles - are the foundation from which all the rest of geometry is built. Triangles are omnipresent and fundamental, appearing in all kinds of contexts, from art and design to engineering and physics.

It is important not only to understand what a triangle is but also to be able to manipulate them effectively. This means being able to calculate their attributes (such as area and perimeter), of course, but also being able to draw precise triangles, choosing the correct sides and angles and recognizing when the given data is impossible.

Context

Mathematics is present in all aspects of everyday life, from the most common to the most complex. Triangles, as a basic shape, play an important role in many aspects of our daily lives. Probably the most relevant is in construction. Triangles are the most stable shape and therefore are used in all kinds of structures, from bridges to the bones in our bodies.

Furthermore, when we learn about the sides of a triangle, we are not only learning about a specific topic in mathematics but also developing logical and critical thinking skills. The relationship between the sides of a triangle is a perfect example of an unchanging mathematical rule. When we understand this, we can begin to grasp the importance and application of mathematical rules in other situations.

To deepen your knowledge about triangles, we suggest reading the following resources:

• Brazil School: Triangles
• World Education: Elements of a Triangle
• Khan Academy: Triangles

Practical Activity

Activity Title: Incredible Triangle - Building and Exploring the Sides of the Triangle

Project Objective:

This project aims to allow students to explore the properties of triangles in a practical and visual way, as well as to integrate geometry concepts with disciplines such as arts and history. Students will also develop socio-emotional skills, such as teamwork, time management, and communication.

Detailed Project Description:

Students will form groups of three to five members to conduct an in-depth study on triangles. They will build various models of triangles, recognizing the necessary conditions for their existence, and will observe how the measurements of the sides can influence the shape of the triangle. They will also analyze the application of triangles in architectural structures and make connections with works of art and historical monuments.

Required Materials:

• Cardboard
• Ruler
• Compass
• Pencil
• Colored pens
• Scissors
• Tape
• Books and reference materials on triangles, architecture, and art
• Internet access
• Camera (optional)

Detailed Step-by-Step for Activity Execution:

1. First, each group must conduct research on the properties of a triangle, focusing on the different types of triangles and the relationship between their sides.

2. With the theory in hand, students must build physical models of triangles (equilateral, isosceles, and scalene), using cardboard and drawing tools.

3. After constructing the triangles, students must make observations and notes about what they notice in terms of the relationship between the sides of the triangles.

4. Now the team will explore how triangles are used in the construction of architectural structures. They should research examples of buildings or structures that use triangles in their design and discuss why triangles may have been used.

5. The next step is to investigate the presence of triangles in works of art and historical monuments. Students should research and document examples of the use of triangles in different artistic and historical contexts.

6. Having collected this information, the group must write a detailed report of their findings. They should divide the report into sections for Introduction, Development, Conclusions, and Bibliography used.

Project Delivery:

The project will be delivered as a report in which students document their entire discovery journey. This document should contain the following parts:

1. Introduction: Contextualization of the theme, its relevance and application in the real world, and the objective of this project.

2. Development: Theory of triangles and the relationship between their sides, details of the practical activity, methodology used, and results obtained.

3. Conclusions: Main learnings and conclusions drawn from the project.

4. Bibliography: Sources used for the project.

In addition to the report, students must deliver the triangle models they built. The project will be complete when all these elements are finished, and students can discuss their findings with confidence and clarity.