### Lesson Plan: Tangency in Technical Drawing
#### Grade Level: Senior Secondary 1
#### Subject: Technical Drawing
#### Duration: 90 minutes
---
**Objective:**
By the end of this lesson, students will be able to:
1. Understand the concept of tangency in technical drawing.
2. Identify points, lines, and circles that are tangent to each other.
3. Draw basic tangent constructions using drafting tools.
---
**Materials Needed:**
- Drawing paper
- Drawing pencils (HB, 2H)
- Erasers
- Drafting rulers
- Compasses
- Protractors
- Set squares
---
### Lesson Outline
#### Introduction (10 minutes)
1. **Welcome and Attendance (2 minutes)**: Greet students and take attendance.
2. **Introduction to Tangency (8 minutes)**:
- Briefly explain what tangency is: the property of a curve (such as a circle) or a surface that touches another curve or surface at exactly one point.
- Discuss real-life examples where tangency is applied (e.g., wheels on a vehicle, gears, and pipe connections).
#### Direct Instruction (20 minutes)
1. **Definitions and Concepts** (10 minutes):
- Point of tangency: The point where a tangent touches a curve.
- Tangent line: A straight line that touches a curve at a single point without crossing it.
- Tangent circle: A circle that touches another circle or a line at exactly one point.
2. **Basic Principles and Rules** (10 minutes):
- The tangent to a circle is perpendicular to the radius at the point of tangency.
- Two circles are tangent if they touch at one point only, either externally (outside each other) or internally (one inside the other).
#### Guided Practice (20 minutes)
1. **Drawing Tangents to a Circle**:
- Step-by-step demonstration on the board.
- Students follow along and draw tangents to given circles on their drawing paper.
2. **Constructing Tangents from a Point Outside a Circle**:
- Use a compass and straightedge to construct two tangents from a point outside a given circle.
- Students practice this technique under teacher guidance.
#### Independent Practice (20 minutes)
1. **Drawing Tangent Circles**:
- Students draw two circles that are tangent internally and two that are tangent externally.
- Instructions to be provided step-by-step. Circulate the room to offer help and check progress.
2. **Complex Tangent Constructions** (if time permits):
- Challenge the students to draw a tangent line to a circle from a point outside the circle, but passing through another given point.
#### Assessment (15 minutes)
1. **Worksheet**:
- Distribute a worksheet with various tangency problems.
- Students complete the worksheet to demonstrate their understanding of tangency constructions.
2. **Peer Review**:
- Students swap their drawings with a partner for peer correction and feedback.
- Encourage constructive feedback and discussion.
#### Closure (5 minutes)
1. **Review**:
- Summarize key takeaways from the lesson.
- Address any remaining questions or concerns.
2. **Homework Assignment**:
- Assign practice problems on tangency from the textbook or a handout.
- Instruct students to compile their work into a portfolio to be submitted in the next class.
3. **Preview Next Lesson**:
- Briefly introduce the next topic (e.g., constructing tangents to two circles) to pique interest.
---
**Notes for Teachers:**
- Ensure all students have the required materials before starting the lesson.
- Keep the pace moderate and check for understanding frequently.
- Encourage students to ask questions and participate actively.
- Provide extra assistance to students who may struggle with using drafting tools.
---
By carefully following this lesson plan, students will gain a strong foundational understanding of tangency in technical drawing, which is critical for more advanced constructions and applications in their future studies.