### Lesson Plan for Technical Drawing: Inscribed and Circumscribed Circles
**Grade Level:** Senior Secondary 1
**Subject:** Technical Drawing
**Duration:** 90 minutes
**Topic:** Inscribed and Circumscribed Circles
#### Objectives:
By the end of this lesson, students will be able to:
1. Understand the concepts of inscribed and circumscribed circles.
2. Identify the center and radius of inscribed and circumscribed circles.
3. Draw inscribed and circumscribed circles for various geometric shapes, especially triangles.
4. Understand and apply the steps involved in constructing these circles technically.
#### Materials Needed:
- Technical drawing instruments (compass, straightedge/ruler, set squares)
- Drawing paper or graph paper
- Pencils, erasers
- Protractors
- Whiteboard and markers (for teacher demonstration)
#### Lesson Structure:
#### **Introduction (10 minutes):**
1. **Greeting and Attendance:** Begin with a warm welcome and take attendance.
2. **Warm-Up Activity:** Ask students to recall basic geometric shapes and their properties, particularly focusing on triangles.
3. **Introduction to the Topic:** Briefly explain what inscribed and circumscribed circles are.
- **Inscribed Circle (Incircle):** A circle that fits perfectly inside a polygon, touching all its sides.
- **Circumscribed Circle (Circumcircle):** A circle that passes through all the vertices of a polygon.
4. **Importance in Technical Drawing:** Explain why understanding these concepts is critical for technical drawing and real-world applications, such as engineering and architecture.
#### **Lesson Development (50 minutes):**
1. **Detailed Explanation and Examples (20 minutes):**
- **Inscribed Circle:**
- Define the incircle in the context of a triangle.
- Explain the steps to find the incenter (the point where the angle bisectors of a triangle intersect) and how to draw the incircle.
- Provide a step-by-step demonstration on the whiteboard.
- **Circumscribed Circle:**
- Define the circumcircle in the context of a triangle.
- Explain the steps to find the circumcenter (the point where the perpendicular bisectors of the sides of a triangle intersect) and how to draw the circumcircle.
- Provide a step-by-step demonstration on the whiteboard.
2. **Interactive Demonstration (10 minutes):**
- Demonstrate how to construct both inscribed and circumscribed circles on the whiteboard.
- Use different types of triangles (acute, obtuse, and right triangles) as examples.
- Encourage students to ask questions during the demonstration.
3. **Guided Practice (20 minutes):**
- Distribute drawing paper and technical drawing instruments to each student.
- Guide students through the process of constructing an inscribed circle:
1. Draw any triangle.
2. Construct the angle bisectors to find the incenter.
3. Use the incenter as the center to draw the incircle with a compass.
- Guide students through the process of constructing a circumscribed circle:
1. Draw any triangle.
2. Construct the perpendicular bisectors of each side to find the circumcenter.
3. Use the circumcenter as the center to draw the circumcircle with a compass.
#### **Conclusion (10 minutes):**
1. **Review:** Summarize the key steps and important points covered in the lesson.
2. **Questions and Answers:** Open the floor for any questions and provide clarifications.
3. **Assessment:** Collect the students' work for assessment. Provide feedback on their constructions to ensure understanding.
4. **Assignment:** Assign a homework task where students must draw inscribed and circumscribed circles for a given set of triangles.
#### **Closure (10 minutes):**
- **Reflection:** Ask a few students to share their thoughts on the lesson. What did they find easy, what was challenging?
- **Preview of Next Lesson:** Give a brief overview of what will be covered in the next lesson.
- **Thank You:** Thank the students for their participation and attention.
By following this lesson plan, students should gain a solid understanding of inscribed and circumscribed circles and be able to apply these concepts in their technical drawing assignments.