Contextualization

The midline and the bisector are fundamental concepts in geometry, a subarea of Mathematics that studies shapes and their properties. The midline of a line segment is the line perpendicular to the segment and passing through its midpoint. It has the characteristic of being a geometric place, which means that it is composed of all points that are equidistant from the ends of the segment.

On the other hand, the bisector of an angle is the half-line that divides the angle into two equal angles. It is also a geometric place and is composed of all points that are at an equal distance from the sides of the angle.

These simple definitions cover the rich applicability of these concepts in the vast field of geometry and in many other disciplines that require the use of spaces and shapes, such as architecture, engineering, and physics.

Importance of the Theme

The bisector and the midline are essential tools for understanding and studying geometry, helping us understand how shapes interact with each other. Moreover, they have practical applications in various areas of knowledge. In architecture, for example, they are used to ensure that buildings are constructed symmetrically, while in engineering, they are used for the design of complex structures.

In everyday life, these concepts are present in various aspects. For example, when cutting a pizza into equal slices, we are using the concept of a bisector. When wanting to find a point equidistant between two locations on the map, we use the concept of a midline.

Practical Activity: The Great Challenge of the Bisector and Midline

Project Objective

This project aims to apply the theoretical knowledge about midline and bisector in solving practical challenges, as well as to stimulate teamwork, creativity, and problem-solving.

Project Description

Students will be divided into groups of 3 to 5 people. Once the groups are formed, each will receive a different challenge, all related to the theme of midline and bisector, which should be solved collaboratively.

The practical activities will focus on the application of the concepts of midline and bisector in everyday situations, allowing students to understand these concepts more deeply and develop problem-solving skills.

Necessary Materials

• Graph paper
• Ruler
• Square
• Compass

Step by Step

1. Group formation: students will be divided into groups of 3 to 5 members.
2. Distribution of challenges: each group will receive a different challenge to be solved, all related to the application of the concepts of bisector and midline.
3. Challenge resolution: the groups will have one week to organize and work on solving the proposed challenges, using the theory learned earlier in class.
4. Documentation of the process: the groups must document the process of solving the challenge, showing how they arrived at the solution and describing the mistakes and successes along the way. This documentation should be presented in the form of a report, containing the following topics:
   • Introduction: The student must contextualize the theme, its relevance and application in the real world, and the objective of this project.
   • Development: The student must explain the theory behind the central themes of the project, explain the activity in detail, indicate the methodology used, and finally present and discuss the results obtained.
   • Conclusion: The student must conclude the work by summarizing its main points, explaining the learnings obtained, and drawing conclusions about the project.
   • Bibliography: The student must indicate the sources they relied on to work on the project such as books, web pages, videos, etc.
5. Presentation of results: at the end of the week, each group must present the final result of their challenge, explaining how they found the solution and what were the learnings acquired during the process. This presentation should be based on the report prepared in Step 4.

Deliverables and Connection with the Practical Activity

At the end of the project, each group must deliver:

1. The solution to the proposed challenge, demonstrating how they applied the concepts of midline and bisector in practice.
2. The report describing in detail the process of solving the challenge, containing the topics of Introduction, Development, Conclusion, and Bibliography.
3. An oral presentation (or remotely, in video format), demonstrating the solution to the challenge and exposing the main learnings.

The report should complement the practical work carried out by the students, detailing the methodology used in solving the challenge, the results obtained, the mistakes and successes along the way, and the learnings acquired. In addition, the report should contain an Introduction section, which contextualizes the theme of the project and its relevance, and a Conclusion section, which summarizes the main points of the work and presents the conclusions drawn about the project.