Objectives (5 - 7 minutes)

• Understand the concept of bisector and perpendicular bisector: The teacher should explain clearly and concisely what bisectors and perpendicular bisectors are. Students should understand that the bisector is the line that divides an angle into two equal parts, while the perpendicular bisector is the line that passes through the midpoint of a segment and is perpendicular to it. Visual examples and practical situations should be presented to facilitate understanding.

• Identify the bisector and perpendicular bisector in geometric figures: After explaining the concept, students should be able to identify and draw bisectors and perpendicular bisectors in geometric figures. The teacher can provide various figures and challenge the students to find these lines.

• Solve problems involving bisectors and perpendicular bisectors: Finally, students should be able to apply the concept of bisectors and perpendicular bisectors in problem-solving. The teacher can present problem situations that require the identification and/or construction of these lines, asking students to solve them individually or in groups.

Secondary Objectives:

• Promote active student participation: The teacher should encourage active student participation during the lesson by asking questions, requesting explanations of their reasoning, and discussing their solutions.

• Develop critical thinking and problem-solving skills: Through problem-solving involving bisectors and perpendicular bisectors, students should develop critical thinking and problem-solving skills.

• Stimulate teamwork: The teacher can organize group activities, promoting collaboration and teamwork. This not only facilitates learning but also develops important social skills.

Introduction (10 - 12 minutes)

• Review of previous content: The teacher should start the lesson by briefly reviewing the concepts of angle, perpendicular lines, and line segment. These concepts are fundamental for understanding the topics that will be covered in the lesson. It is important that students are familiar with these concepts, as they will be used in the definition and application of bisectors and perpendicular bisectors.

• Problem situation 1: The teacher can present the following situation: 'Imagine you have a pizza and want to divide the crust into equal parts. How would you do that with just one cut?' This situation serves to introduce the concept of bisector. The teacher can ask students to draw the pizza and indicate where the cut would be made.

• Problem situation 2: Next, the teacher can present the following situation: 'Now, imagine you have a piece of yarn and want to find the exact middle of it. How would you do that without a ruler or a scale?' This situation serves to introduce the concept of perpendicular bisector. The teacher can ask students to draw the piece of yarn and indicate where the perpendicular bisector would pass.

• Contextualization of the importance of the subject: The teacher should explain that the concept of bisector and perpendicular bisector is not only applicable in drawings or geometry. They are widely used in various areas such as architecture, design, engineering, among others. For example, when building a bridge, engineers need to ensure that the pillars are aligned with the perpendicular bisector of the segment they support to ensure the stability of the structure.

• Introduction of the topic: Finally, the teacher should introduce the topic of the lesson, explaining that bisectors and perpendicular bisectors will be addressed, how to identify them in geometric figures, and how to apply them in problem-solving. The teacher can emphasize that although the concepts may seem complex at first, they will be easily understood with practice and the use of visual examples.

Development (20 - 25 minutes)

• Theory and Concepts (10 - 12 minutes):

  1. Definition of Bisector and Perpendicular Bisector (3 - 5 minutes): The teacher should start the explanation by defining what bisectors and perpendicular bisectors are, reinforcing that the bisector is the line that divides an angle into two equal parts, and the perpendicular bisector is the line that passes through the midpoint of a segment and is perpendicular to it. The definitions should be clear and concise, and the teacher can use drawings to illustrate each concept.
  2. Construction of Bisector and Perpendicular Bisector (3 - 4 minutes): The teacher should then show how to construct a bisector and a perpendicular bisector. For the bisector, the teacher can explain that two arcs with the same radius should be drawn from the points where the sides of the angle intersect, and that the bisector is the line that passes through the vertex of the angle and the point where the arcs intersect. For the perpendicular bisector, the teacher can explain that two arcs with the same radius should be drawn from the ends of the segment, and that the perpendicular bisector is the line that passes through the midpoint of the segment and the point where the arcs intersect.
  3. Properties of Bisectors and Perpendicular Bisectors (3 - 4 minutes): The teacher should then discuss some properties of bisectors and perpendicular bisectors. For example, the teacher can explain that in a triangle, the bisectors meet at a point called the incenter, and that the perpendicular bisector of a side of a triangle is perpendicular to that side and passes through the midpoint. The teacher can also discuss how these lines are used to solve practical problems, such as dividing an angle into equal parts or locating the midpoint of a segment.

• Practice (10 - 13 minutes):

  1. Problem Solving (5 - 7 minutes): The teacher should present students with some problems involving the construction and use of bisectors and perpendicular bisectors. The problems should be varied and challenging, but at the same time accessible to students. The teacher should encourage students to discuss the problems in groups, promoting collaboration and the exchange of ideas. After some time, the teacher should ask a representative from each group to present the solution to the problem to the class, and should foster discussion about the different approaches to solving the problem.
  2. Practical Activity (5 - 6 minutes): The teacher should then propose a practical activity in which students will have to construct bisectors and perpendicular bisectors in geometric figures. The teacher can provide pre-drawn figures and ask students to identify and construct the bisectors and perpendicular bisectors. At the end of the activity, the teacher should correct the answers and clarify any doubts students may have.

Return (8 - 10 minutes)

• Review of Concepts (3 - 4 minutes): After the practice, the teacher should review the main concepts of the lesson, reaffirming the definitions of bisector and perpendicular bisector, and the properties associated with them. The teacher can do this through an oral summary, or by writing the concepts on a board or slide presentation. It is important that students have a clear understanding of these concepts before moving on to the next stage of the lesson.

• Connection with Theory (2 - 3 minutes): Next, the teacher should make the connection between theory and practice, explaining how the concepts of bisector and perpendicular bisector were applied in solving problems and in the practical activity. The teacher can highlight examples of how these concepts are used in everyday life, in areas such as architecture, design, engineering, among others. This helps reinforce the importance of the subject and motivates students to continue learning.

• Individual Reflection (2 - 3 minutes): The teacher should then propose that students reflect individually on what they learned in the lesson. The teacher can ask questions like: 'What was the most important concept you learned today?' and 'What questions have not been answered yet?' Students should be encouraged to think about these questions and write down their answers.

• Group Discussion (1 minute): To end the lesson, the teacher can ask some students to share their answers with the class. This not only helps consolidate learning but also allows the teacher to assess students' understanding and identify any areas that may need review or reinforcement.

• Feedback and Closure (1 minute): The teacher should thank the students for their participation and effort, and should encourage them to continue studying the subject. The teacher can also ask for feedback on the lesson to help improve future lessons. For example, the teacher can ask: 'What did you think of the lesson content?' or 'Was there any part of the lesson that you found difficult to understand?'

Conclusion (5 - 7 minutes)

• Summary of Contents (2 - 3 minutes): The teacher should start the Conclusion by summarizing the main points covered in the lesson. He should review the definition of bisector and perpendicular bisector, the properties associated with these lines, and how to construct them. The teacher can do this orally or through a board or slide presentation. The goal is to reinforce the concepts learned and ensure that students have understood the material.

• Theory-Practice Connection (1 - 2 minutes): Next, the teacher should emphasize how the lesson connected theory with practice. He should review the problems solved and the practical activity, and how the concepts of bisector and perpendicular bisector were applied in these situations. The teacher can highlight the importance of understanding theory to solve practical problems, and how practice helps solidify the understanding of theory.

• Additional Materials (1 minute): The teacher can suggest some additional study materials for students who wish to deepen their knowledge on the subject. This may include math books, educational websites, explanatory videos, among others. The teacher can share these resources with students through an online platform, such as a school website or a virtual learning environment.

• Everyday Applications (1 minute): Finally, the teacher should briefly discuss some practical applications of the concept of bisector and perpendicular bisector in everyday life. He can mention, for example, how these lines are used in architecture to ensure symmetry and stability of structures, or in design to create shapes and patterns. This helps show students the relevance of what they are learning and how mathematics is present in their lives.

• Closure (1 minute): To conclude the lesson, the teacher should thank the students for their participation and effort. He can reinforce the importance of continuing to study and practice the subject, and that he will be available to clarify any doubts that may arise. The teacher should also encourage students to prepare for the next lesson by reviewing the material and solving additional problems, if possible.