Contextualization

Geometry has a significant presence in our daily lives, whether in building construction, structure design, city mapping, or even in art. Understanding geometric concepts is much more than just a requirement of the school curriculum; it is a way to better understand the world around us. And that's where quadrilaterals come in - geometric figures with four sides. Knowing their properties, especially those related to angles, is essential for a full appropriation of geometric knowledge.

Geometric figures with four sides, such as the square, rectangle, parallelogram, rhombus, and trapezoid, are common examples of quadrilaterals. Each of these quadrilaterals has unique properties related to their internal angles, which we will explore in this project.

Theoretical Introduction

Let's start by reviewing what angles are. An angle is formed by two rays with a common point, which we call a vertex. The measure of angles is given in degrees and ranges from 0 to 360. One of the fundamental concepts in plane geometry is that the sum of the internal angles of a polygon is determined by the number of sides it has.

When we talk about quadrilaterals, we are talking about polygons with four sides. And here is the key point we will explore: the sum of the internal angles of any quadrilateral always adds up to 360 degrees, regardless of the shape and size of the quadrilateral. This is a fundamental property of quadrilaterals, and it is something that you will be able to observe, test, and prove for yourselves throughout this project.

Finally, but not least, it is necessary to understand that the angles of a quadrilateral do not need to be all equal for the sum to be 360 degrees. There are quadrilaterals with all internal angles equal (like the square and rectangle), and others where all angles are different (like the trapezoid).

Atividade Prática

Activity Title: "Quadrilaterals Angles: A Practical Investigation"

Project Objective

Learn and verify the properties of quadrilateral angles through a practical and fun activity, culminating in the production of a detailed report on the project.

Detailed Project Description

Students, divided into groups of 3 to 5, should build various types of quadrilaterals, experiment with different angle configurations, and then measure and sum the internal angles. They should also create a visual representation of the results, demonstrating how the internal angles of quadrilaterals always add up to 360 degrees, regardless of the type of quadrilateral.

At a later stage, students should explore in more depth two specific types of quadrilaterals: the parallelogram and the trapezoid. The idea is for them to carry out experiments, cutting and rearranging the parts of the figures to form other known polygons (such as triangles and rectangles), in order to observe the congruence between the internal angles of these figures and the angles of the original quadrilaterals.

Finally, students will be encouraged to seek real-world applications for the concept of angles in quadrilaterals.

Required Materials

• Cardboard paper of various colors
• Ruler
• Compass
• Protractor
• Scissors
• Glue
• Pencils and pens
• Camera to document the process

Detailed Step-by-Step for Activity Execution

1. Research and discuss in groups the different types of quadrilaterals and their properties.
2. Draw and cut out at least three different types of quadrilaterals, of varying sizes, on cardboard paper.
3. Use the protractor to accurately measure the internal angles of each created quadrilateral.
4. Record the angle measurements and calculate the total sum.
5. Verify if the sum of the internal angles of the created quadrilaterals is equal to 360 degrees.
6. Create a visual representation of the results, whether a graph, a table, or another form of your choice.
7. Conduct an in-depth exploration with the parallelogram and trapezoid. Cut them into triangles, rearrange them, and observe the congruence of the angles.
8. Research and discuss practical applications of angles in quadrilaterals in the real world.
9. Create a project report according to the guidelines for the final submission.

Project Deliverables

The group must submit a detailed project report, containing the following sections:

1. Introduction: Contextualization on the topic, the relevance of angles in quadrilaterals, practical applications, and the project's objective.
2. Development: Detailed explanation of the theory behind angles in quadrilaterals, explanation of the entire process carried out in the practical activity, from conception, methodology used, to the presentation and discussion of the results achieved.
3. Conclusions: Recap of the main points, showing the acquired learnings and conclusions drawn from the project.
4. Bibliography: Indication of the resources used to support the project.

The report should be clear, precise, organized, and demonstrate mastery of the concepts studied and applied in the practical activity. Illustrate the theory with the data collected in the practical experience and with the real-world applications researched. Use photos and diagrams to illustrate the procedures and results.