# Lesson Plan: Escribed Circle in Technical Drawing
## Grade Level
Senior Secondary 1
## Subject
Technical Drawing
## Duration
2 Hours
## Topic
Escribed Circle (Excircle)
## Objectives
By the end of the lesson, students will be able to:
1. Define and explain what an escribed circle (excircle) is.
2. Identify the properties of an escribed circle.
3. Construct an escribed circle for a given triangle using technical drawing tools.
4. Understand and apply the practical significance of escribed circles in real-world scenarios.
## Materials Needed
- Drawing paper
- Drawing board
- Set squares
- Compass
- Ruler
- Protractor
- Pencils (HB and 2H)
- Eraser
- Sharpener
## Pre-requisites
Students should have prior knowledge of:
- Basic geometric constructions
- Properties of triangles
- Use of technical drawing tools
## Lesson Activities
### Introduction (15 Minutes)
1. **Greeting and Introduction:** Begin the class with a warm welcome and briefly introduce the topic.
2. **Definition and Explanation:** Provide a clear definition of an escribed circle. Explain that an escribed circle (or excircle) is a circle that lies outside a triangle and is tangent to one of its sides and the extensions of the other two.
3. **Properties of Escribed Circles:** Discuss the key properties:
- An escribed circle is associated with each vertex of the triangle.
- It touches one side of the triangle and the extensions of the other two sides.
- The center of an escribed circle is called an excenter.
### Demonstration (20 Minutes)
1. **Step-by-Step Construction:**
- Draw a given triangle ABC.
- Extend the sides AB and AC.
- Construct the internal angle bisectors of angles B and C to find their intersection at I (the incenter of the triangle).
- Draw perpendiculars from I to the sides AB, BC, and AC.
- Use the point of intersection of these perpendiculars and the opposite sides to find the excenters (Ia, Ib, Ic).
- Use a compass to draw circles from each excenter passing through the respective tangent points.
2. **Illustrative Example:** Demonstrate the construction on the board, explaining each step clearly.
### Guided Practice (30 Minutes)
1. **Class Activity:** Provide students with triangles to practice constructing the escribed circles (excircles). Walk around to offer assistance and check for understanding.
2. **Peer Review:** Allow students to pair up and review each other's work, ensuring they follow the proper steps.
### Independent Practice (25 Minutes)
1. **Worksheet:** Hand out a worksheet with different types of triangles for students to construct escribed circles independently.
2. **Application Activity:** Pose real-world problems where the use of escribed circles can be applied, e.g., constructing gardens or roundabouts tangent to roads.
### Conclusion (15 Minutes)
1. **Recap:** Summarize the key points of the lesson, reiterating the importance and application of escribed circles.
2. **Q&A Session:** Open the floor for any questions to clarify doubts.
3. **Assignment:** Assign homework to construct escribed circles for given triangles and describe their significance in various engineering fields.
### Assessment (5 Minutes)
1. **Quick Quiz:** Conclude with a quick quiz to assess students' understanding:
- Define an escribed circle.
- Explain how to find the excenter.
- List some practical applications of escribed circles.
## Homework
1. Construct escribed circles for different types of triangles (scalene, isosceles, and equilateral) and submit your drawings.
2. Write a brief essay on the importance of escribed circles in civil engineering and architecture.
## Reflection
- Reflect on the lesson’s effectiveness. Did students understand the concept? Were they able to apply the skills taught?
- Note areas for improvement in future lessons.
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This lesson plan aims to provide a comprehensive understanding of escribed circles while incorporating practical applications to engage students in the subject matter effectively.