Class: Junior Secondary School 2 (JSS2, JSS 2)
Term: 1st Term
Week: 9
Age: 13 years
Duration: 45 minutes
Subject: Basic Science And Technology
Curriculum Theme: Basic Technology
Previous Lesson: Definition and Types of Triangles
Topic: Triangles (Part 2)
Subject Matter: Construction of triangles, Circumscribing, Inscribing, Escribing circles to a given triangle

Specific Objectives

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

Cognitive Domain:
(a) Describe how to construct different types of triangles accurately.
(b) Explain the processes of circumscribing, inscribing, and escribing circles to a triangle.
Affective Domain:
(a) Appreciate the importance of accuracy and neatness in technical drawing.
Psychomotor Domain:
(a) Construct various types of triangles using appropriate drawing instruments.
(b) Draw circumscribed, inscribed, and escribed circles to a given triangle.
Social Domain:
(a) Work cooperatively in pairs or groups to complete construction tasks.

Reference Materials

The following resources was used in planning this lesson:

9 Years Basic Education Curriculum
Lagos State Unified Scheme of work for Junior Secondary Schools
BYJU’S – “Construction of Triangles” (https://byjus.com/maths/construction-of-triangles)
Cuemath – “Construction of Triangles in Geometry” (https://www.cuemath.com/geometry/construction-of-triangles)
Relevant Textbooks

Instructional Materials

The teacher will teach this lesson with the aid of:

Pair of compasses
Ruler and set squares
Protractor
Drawing board and pencils
Chart of different types of triangles
Prepared drawings of circumscribed, inscribed, and escribed circles

Rationale for the Lesson

This lesson equips pupils with essential drawing skills in constructing triangles and related circles, which are foundational for technical drawing and engineering studies.

Prerequisite/Previous Knowledge

Pupils have already learned the basic properties and construction of triangles in previous lessons and can use drawing instruments to construct simple geometrical figures.

Lesson Content/Board Summary

Triangles

Construction of Triangles

In geometry, triangles can be constructed when certain measurements such as sides and angles are given. Constructions are done with drawing instruments to ensure accuracy.

The following are methods of constructing triangles:

Construction of a triangle when three sides are given (SSS).
Construction of a triangle when two sides and the included angle are given (SAS).
Construction of a triangle when two angles and the included side are given (ASA).
Construction of a right-angled triangle when hypotenuse and one side are given.

Circumscribing a Circle to a Triangle

A circumscribed circle of a triangle is a circle drawn around the triangle passing through all its three vertices. The center of the circle is the point where the perpendicular bisectors of the sides meet.

The following are steps in circumscribing a circle to a triangle:

Construct the given triangle.
Draw the perpendicular bisectors of at least two sides.
The point of intersection is the center of the circle.
With the center and radius, draw the circumscribed circle passing through the vertices.

Inscribing a Circle in a Triangle

An inscribed circle of a triangle is a circle drawn inside the triangle touching all three sides. Its center is the point where the angle bisectors of the triangle meet.

The following are steps in inscribing a circle in a triangle:

Construct the given triangle.
Draw the angle bisectors of at least two angles.
The point of intersection is the center of the inscribed circle.
With the center and radius, draw the circle that touches all sides internally.

Escribing a Circle to a Triangle

An escribed circle of a triangle is a circle drawn outside the triangle, touching one side of the triangle externally and extending the other two sides. Each triangle has three escribed circles.

The following are steps in escribing a circle to a triangle:

Construct the given triangle.
Draw the internal bisector of one angle and external bisectors of the other two angles.
The point of intersection is the center of the escribed circle.
With the center and radius, draw the circle touching one side externally.

Teaching Methods/Instructional Techniques:

Discussion, Lecture, Explanation, Demonstration, Guided Practice, Group Work, Question and Answer, Use of Visual Aids

Instructional Procedures

To deliver this lesson, the teacher will adopt the following steps:

Step 1: Introduction

Time: 5 minutes
Teaching Skill: Set Induction
Teacher’s Activity: Teacher revises the previous lesson on basic triangle constructions by asking pupils to recall methods of constructing a triangle with given measurements.
Pupils’ Activity: Pupils respond to questions on triangle constructions.
Learning Point: Pupils recall basic knowledge of triangle construction.

Step 2: Construction of Various Triangles

Time: 10 minutes
Teaching Skill: Explanation and Demonstration
Teacher’s Activity: Teacher demonstrates the construction of triangles using different conditions (SSS, SAS, ASA, right-angled triangle).
Pupils’ Activity: Pupils observe and practice the constructions with instruments.
Learning Point: Pupils learn accurate methods of constructing different types of triangles.

Step 3: Circumscribing a Circle

Time: 8 minutes
Teaching Skill: Demonstration
Teacher’s Activity: Teacher demonstrates steps in circumscribing a circle around a triangle.
Pupils’ Activity: Pupils follow steps and attempt the construction.
Learning Point: Pupils understand how to construct circumscribed circles.

Step 4: Inscribing and Escribing Circles

Time: 10 minutes
Teaching Skill: Explanation and Guided Practice
Teacher’s Activity: Teacher explains and demonstrates the steps in inscribing and escribing circles to a given triangle.
Pupils’ Activity: Pupils practice the construction under guidance.
Learning Point: Pupils learn and apply methods of inscribing and escribing circles to triangles.

Step 5: Note-Taking

Time: 5 minutes
Teaching Skill: Explanation
Teacher’s Activity: Teacher dictates or writes board summary for pupils to copy.
Pupils’ Activity: Pupils copy notes into their exercise books.
Learning Point: Pupils have a written record of the lesson.

Step 6: Evaluation/Review

Time: 5 minutes
Teaching Skill: Questioning
Teacher’s Activity: The teacher evaluates the learning by asking the following questions:

State two methods of constructing a triangle.
Explain how to construct a circumscribed circle of a triangle.
What is the difference between an inscribed and an escribed circle?
Pupils’ Activity: Pupils respond orally to evaluation questions.
Learning Point: Pupils demonstrate understanding of triangle constructions and related circles.

Step 7: Conclusion

Time: 2 minutes
Teaching Skill: Reinforcement
Teacher’s Activity: Teacher summarizes the lesson, emphasizes accuracy in drawing, and encourages further practice.
Pupils’ Activity: Pupils listen attentively.
Learning Point: Pupils consolidate knowledge of triangle constructions and circle constructions.

Lesson Keywords

Construction – process of drawing shapes using instruments
Circumscribed circle – a circle passing through all vertices of a triangle
Inscribed circle – a circle touching all sides of a triangle internally
Escribed circle – a circle drawn outside a triangle touching one side externally
Bisector – a line that divides an angle or line segment into two equal parts

Differentiation

Provide step-by-step guidance for slower learners and allow advanced pupils to assist others. Use charts and pre-drawn diagrams to reinforce understanding.

Note for teachers using this lesson plan

Ensure pupils handle drawing instruments properly for accuracy. Encourage neatness and correct errors immediately. Allow time for adequate practice in class.