Lesson Plan | Lesson Plan Tradisional | Bisector and Perpendicular Bisector

Objectives

Duration: 10 - 15 minutes

The aim of this stage is to lay a strong foundation for students by introducing the core concepts of angle bisectors and perpendicular bisectors. This will allow students to appreciate the significance of these geometric features and how they apply in various scenarios. By the conclusion of this stage, students should be ready to recognize and apply these concepts in geometric problem-solving, leading to a clearer understanding in the subsequent parts of the lesson.

Objectives Utama:

1. Grasp the concept of angle bisector and perpendicular bisector as geometric loci.

2. Identify perpendicular bisectors and angle bisectors in various geometric shapes.

3. Understand the practical application of angle bisectors and perpendicular bisectors in solving geometric problems.

Introduction

Duration: 10 - 15 minutes

🎯 Purpose: The goal of this stage is to firmly establish the foundational concepts of angle bisectors and perpendicular bisectors. By the end, students should be equipped to identify and utilize these concepts in solving geometric problems.

Did you know?

🤔 Curiosity: Did you know that angle bisectors play a crucial role in architecture and design for achieving perfect symmetry in structures? For instance, when drafting the blueprints for a home, architects often utilize angle bisectors to ensure even division of angles, resulting in balanced and visually appealing designs. The perpendicular bisector is equally important in civil engineering, as it helps to find equidistant points between two locations, such as while constructing bridges or roads.

Contextualization

📍 Context: Begin the lesson by emphasizing the importance of lines and segments in geometry. Explain that while studying geometric shapes, one must understand how certain lines can divide or connect parts of those shapes. Introduce the concepts of angle bisector and perpendicular bisector as vital lines in geometry. Mention that today, we will dive deep into these lines, exploring their properties and how to spot them in various geometric figures.

Concepts

Duration: 40 - 45 minutes

🎯 Purpose: This stage aims to give students a comprehensive understanding of angle bisectors and perpendicular bisectors, including their definitions and properties. By the end, students should be capable of identifying and applying these concepts in various geometric figures and tackling relevant problems, using the skills they've acquired.

Relevant Topics

**1. 📏 Definition of Angle Bisector: Explain that the angle bisector of an angle is the ray that divides the angle into two equal parts. Emphasize that the angle bisector is the set of points that are equidistant from the sides of the angle. Provide practical examples of angle bisectors in triangles and other polygons.

🔍 **Properties of Angle Bisector:**
Discuss how the angle bisector in a triangle divides the opposite side into segments that are proportional to the adjacent sides.
Introduce the Internal Angle Bisector Theorem and explain its application in solving geometric problems.

📐 **Definition of Perpendicular Bisector:**
Define the perpendicular bisector of a segment as the line that intersects the segment at a right angle through its midpoint.
Point out that the perpendicular bisector is the locus of points equidistant from the endpoints of the segment.
Demonstrate examples of perpendicular bisectors in squares and other shapes.

🔍 **Properties of Perpendicular Bisector:**
Explain that the perpendicular bisector of a segment in a triangle finds points that are equidistant from the triangle’s vertices.
Teach the Perpendicular Bisector Theorem and its use in solving geometric problems.**

To Reinforce Learning

1. Where is the angle bisector located in a 90-degree angle within an isosceles triangle? Explain your reasoning.

2. If you have a line segment AB, how would you go about finding the perpendicular bisector? Describe the steps and explain its significance.

3. In triangle ABC, if the angle bisector of angle A intersects side BC at D, and AB = 6 cm, AC = 8 cm, and BC = 10 cm, what are the lengths of segments BD and DC? Use the Angle Bisector Theorem.

Feedback

Duration: 20 - 25 minutes

🎯 Purpose: This stage is designed to solidify the knowledge gained by students during the lesson, providing an opportunity for them to reflect and discuss. Students can clarify doubts, reinforce their understanding, and apply what they've learned in new scenarios. This stage also promotes active participation and critical thinking, fostering a collaborative and enriching learning experience.

Diskusi Concepts

1. Where is the angle bisector situated in a 90-degree angle of an isosceles triangle? Explain your answer. The angle bisector in a 90-degree isosceles triangle divides the angle into two 45-degree angles. The two sides next to the 90-degree angle are equal, making the bisector perpendicular to the triangle's base, hence splitting it into two congruent right-angled triangles.

How do you find the perpendicular bisector of a segment AB? Describe the steps involved and the importance of the perpendicular bisector. To find the perpendicular bisector of segment AB, do the following: 1. Locate the midpoint of AB, which is equidistant from points A and B. 2. Draw a line perpendicular to segment AB that passes through the midpoint. This line is the perpendicular bisector. The significance of the perpendicular bisector lies in its property as the set of points equidistant from the endpoints of segment AB, indicating that every point on the perpendicular bisector is equidistant from A and B.

In triangle ABC, if the angle bisector of angle A intersects side BC at D and AB = 6 cm, AC = 8 cm, and BC = 10 cm, what are the lengths of BD and DC? Use the Angle Bisector Theorem. Applying the Internal Angle Bisector Theorem: (\frac{AB}{AC} = \frac{BD}{DC}) Substituting the values: (\frac{6}{8} = \frac{BD}{DC}) Simplifying gives: (\frac{3}{4} = \frac{BD}{DC}) Thus, BD is 3 parts and DC is 4 parts of a total of 7 parts of segment BC, which is 10 cm. Therefore: BD = (\frac{3}{7} \times 10 \approx 4.29 \text{ cm}) DC = (\frac{4}{7} \times 10 \approx 5.71 \text{ cm})

Engaging Students

1. Can you identify the angle and perpendicular bisectors in other geometric shapes apart from triangles? Provide examples. 2. How might the concept of the perpendicular bisector assist in tackling real-world issues, such as finding midpoints between two towns? 3. Discuss how angle bisectors can contribute to precise and symmetrical designs in construction. 4. What are other practical uses of the perpendicular bisector that you can envision in fields like engineering and design? 5. If the angle bisector creates equal segments, how does this affect symmetry in mirrored images?

Conclusion

Duration: 10 - 15 minutes

The purpose of this phase is to summarize and cement the key points discussed in the lesson, strengthening students' comprehension. Additionally, it connects theory with practice, showcasing how the concepts learned are important in both everyday situations and professional contexts, while encouraging students to apply their newfound knowledge practically.

Summary

['The angle bisector of an angle is the ray that divides it equally.', "The angle bisector represents points equidistant from the angles' sides.", 'The perpendicular bisector of a segment is the line that meets the segment at a right angle through its midpoint.', "The perpendicular bisector is a locus of points that are equidistant from the segment's endpoints.", 'In a triangle, the angle bisector divides the opposite side proportionally to the adjacent sides.', "In a triangle, the perpendicular bisector locates points equidistant from the triangle's vertices."]

Connection

Throughout the lesson, theoretical concepts regarding angle bisectors and perpendicular bisectors were connected to practical situations using clear examples and geometric problems. Real-world applications were discussed in geometric shapes, such as triangles and squares, emphasizing how these concepts are crucial in fields like architecture and civil engineering, reinforcing their significance in everyday life.

Theme Relevance

Understanding angle and perpendicular bisectors is imperative not just for highlighting geometric concepts but also for their real-world implications. For example, angle bisectors assure precision and symmetry in construction, while perpendicular bisectors are critical in engineering for determining equidistant points, aiding in the planning of roads and bridges. These insights deepen our understanding of geometry in the world around us.