Class: Senior Secondary School 1 (SS1, SS 1, SSS1, SSS 1)
Term: 1st Term
Week: 9
Age: 15 years
Duration: 45 minutes
Subject: Technical Drawing
Curriculum Theme: Technical Drawing
Previous Lesson: Circle and Its Parts.
Topic: CIRCLE AND TRIANGLES
Subject Matter: construction of inscribed circle in a triangle, construction of circumscribed circle about a triangle, construction of ascribed circle to a triangle, use of angle bisectors and perpendicular bisectors in constructions

Specific Objectives

By the end of the lesson, pupils should be able to:

Cognitive Domain:

Define inscribed, circumscribed, and ascribed circles.
Explain the steps involved in constructing each type of circle in relation to a triangle.
State the role of angle bisectors and perpendicular bisectors in these constructions.

Affective Domain:

Appreciate the precision required in geometric constructions.
Pay attention to details during the demonstration and practical work.

Psychomotor Domain:

Accurately construct an inscribed circle in a given triangle.
Accurately construct a circumscribed circle about a given triangle.
Accurately construct an ascribed circle to a given triangle.
Label all construction lines and relevant points correctly.

Collaborate with peers when discussing construction challenges.

Reference Materials

The following resources were used in planning this lesson:

9 Years Basic Education Curriculum for Technical Drawing.
State Unified Scheme of Work for Technical Drawing SSS 1.
Adeyemi, A. A. (2010). Technical Drawing for Senior Secondary Schools. Evans Brothers (Nigeria Publishers) Limited.
https://www.waeconline.org.ng/
https://www.nerdc.gov.ng/

Instructional Materials

The teacher will teach this lesson with the aid of:

Drawing instruments (set square, protractor, divider, pencil)
Compasses
Ruler
Drawing paper
Chalkboard and chalk

Rationale for the Lesson

This lesson helps pupils understand how to construct different types of circles related to triangles. It builds foundational technical drawing skills and applies geometric principles to practical drawing tasks.

Prerequisite/Previous Knowledge

Pupils should have prior knowledge of basic geometric shapes, types of triangles, and how to use various drawing instruments like compasses and rulers for basic constructions such as bisecting lines and angles.

Lesson Content/Board Summary

CIRCLE AND TRIANGLES

Introduction to Bisectors

Geometric constructions often require the use of bisectors to locate specific points.

The following are important types of bisectors:

Angle Bisector: A line that divides an angle into two equal parts. The intersection of angle bisectors gives the center of an inscribed circle.
Perpendicular Bisector: A line that divides a line segment into two equal parts at a 90-degree angle. The intersection of perpendicular bisectors of the sides of a triangle gives the center of a circumscribed circle.

Inscribed Circle (Incircle) in a Triangle

An inscribed circle is a circle drawn inside a triangle such that it touches all three sides of the triangle at a single point each. The center of the inscribed circle is called the incenter.

The steps to construct an inscribed circle in a triangle are:

Draw the given triangle (e.g., ABC).
Bisect any two interior angles of the triangle (e.g., angle A and angle B).
The point where the two angle bisectors intersect is the incenter (I) of the triangle.
From the incenter (I), draw a perpendicular line to any one side of the triangle (e.g., AB). Let the point of intersection be D.
With I as the center and ID as the radius, draw a circle. This circle will touch all three sides of the triangle.

Circumscribed Circle (Circumcircle) about a Triangle

A circumscribed circle is a circle that passes through all three vertices of a triangle. The center of the circumscribed circle is called the circumcenter.

The steps to construct a circumscribed circle about a triangle are:

Draw the given triangle (e.g., ABC).
Construct the perpendicular bisectors of any two sides of the triangle (e.g., AB and BC).
The point where the two perpendicular bisectors intersect is the circumcenter (O) of the triangle.
With O as the center and the distance from O to any vertex (e.g., OA) as the radius, draw a circle. This circle will pass through all three vertices of the triangle.

Ascribed Circle (Excircle) to a Triangle

An ascribed circle is a circle that touches one side of a triangle externally and the extensions of the other two sides. A triangle has three ascribed circles, one for each side.

The steps to construct an ascribed circle to a triangle (e.g., opposite side BC) are:

Draw the given triangle (e.g., ABC).
Extend the two sides adjacent to the chosen side (e.g., extend AB and AC).
Bisect the exterior angles formed by the extended sides (e.g., at vertex B and C).
Bisect the interior angle of the vertex opposite the chosen side (e.g., angle A).
The point where these three bisectors intersect is the excenter (E).
From the excenter (E), draw a perpendicular line to the side it touches externally (e.g., BC). Let the point of intersection be F.
With E as the center and EF as the radius, draw a circle. This circle will touch the side BC externally and the extensions of AB and AC.

Teaching Methods/Instructional Techniques

Discussion, Lecture, Demonstration, Question and Answer, Visual Aids

Instructional Procedures

Step 1: Introduction

Time: 5 minutes
Teaching Skill: Set Induction
Teacher’s Activity: The teacher greets the pupils and reviews the previous lesson briefly. The teacher then introduces the new topic, “Circle and Triangles,” by asking pupils if they know circles can be drawn inside or around triangles.
Pupils’ Activity: Pupils respond to questions and listen attentively to the introduction.
Learning Point: Pupils are prepared for the new lesson and connect it to prior knowledge.

Step 2: Review of Bisectors

Time: 7 minutes
Teaching Skill: Explanation/Demonstration
Teacher’s Activity: The teacher explains the concepts of angle bisectors and perpendicular bisectors, demonstrating how to construct them on the board. The teacher highlights their importance in finding the centers of circles related to triangles.
Pupils’ Activity: Pupils observe the demonstration, ask questions, and take notes.
Learning Point: Pupils recall and reinforce their understanding of angle and perpendicular bisectors.

Step 3: Construction of Inscribed Circle

Time: 10 minutes
Teaching Skill: Demonstration/Guidance
Teacher’s Activity: The teacher draws a triangle on the board and demonstrates step-by-step how to construct an inscribed circle using angle bisectors. The teacher ensures clarity in each step and labels all construction lines.
Pupils’ Activity: Pupils carefully follow the teacher’s demonstration, attempting to replicate the construction on their drawing papers.
Learning Point: Pupils learn the procedure for constructing an inscribed circle and its center (incenter).

Step 4: Construction of Circumscribed Circle

Time: 10 minutes
Teaching Skill: Demonstration/Guidance
Teacher’s Activity: The teacher draws another triangle and demonstrates the construction of a circumscribed circle using perpendicular bisectors of the sides. Emphasis is placed on the circumcenter and its equidistant relationship to the vertices.
Pupils’ Activity: Pupils observe the demonstration and attempt the construction on their drawing papers.
Learning Point: Pupils learn the procedure for constructing a circumscribed circle and its center (circumcenter).

Step 5: Construction of Ascribed Circle

Time: 8 minutes
Teaching Skill: Demonstration/Explanation
Teacher’s Activity: The teacher explains what an ascribed circle is and demonstrates the construction of one ascribed circle for a triangle, showing how it touches one side externally and the extensions of the other two sides. The teacher explains the use of exterior angle bisectors.
Pupils’ Activity: Pupils observe the demonstration and ask clarifying questions.
Learning Point: Pupils understand the concept and construction of an ascribed circle and its center (excenter).

Step 6: Evaluation/Review

Time: 5 minutes

Teaching Skill: Questioning/Assessment

Teacher’s Activity: The teacher evaluates the learning by asking the following questions:

Define an inscribed circle.
State two steps for constructing an inscribed circle in a triangle.
What is the center of a circumscribed circle called?
Explain how to locate the center of an ascribed circle.

Pupils’ Activity: Pupils answer orally and in writing.

Learning Point: Pupils demonstrate understanding of the lesson.

Step 7: Conclusion

Time: 5 minutes
Teaching Skill: Summarization/Assignment
Teacher’s Activity: The teacher summarizes the key points of the lesson, reiterating the importance of bisectors in geometric constructions. The teacher assigns homework: pupils are to construct all three types of circles (inscribed, circumscribed, and one ascribed) for a given triangle in their notebooks.
Pupils’ Activity: Pupils listen to the summary and copy the homework assignment.
Learning Point: Pupils consolidate their learning and are provided an opportunity for practice.

Lesson Keywords

Inscribed Circle – A circle drawn inside a triangle touching all three sides.
Circumscribed Circle – A circle drawn around a triangle passing through all three vertices.
Ascribed Circle – A circle touching one side of a triangle externally and the extensions of the other two sides.
Angle Bisector – A line that divides an angle into two equal parts.
Perpendicular Bisector – A line that divides a line segment into two equal parts at a 90-degree angle.
Incenter – The center of an inscribed circle.
Circumcenter – The center of a circumscribed circle.
Excenter – The center of an ascribed circle.

Differentiation

For pupils who grasp concepts quickly, the teacher can challenge them to construct an equilateral or isosceles triangle and then construct all three circles, noting any special observations. For pupils requiring additional support, the teacher can provide pre-drawn triangles or step-by-step handouts and offer more individualized guidance during practical sessions.

Note for teachers using this lesson plan

Ensure that all pupils have complete and functional drawing instruments. Emphasize the precision required in making constructions. Walk around the classroom during practical activities to provide individual assistance and correct mistakes promptly. Encourage pupils to use light construction lines that can be erased or drawn over cleanly.