Mastering Triangle Constructions and Circle Placements in Geometry Basic Technology JSS 2 First Term Lesson Notes Week 10

Basic Technology JSS 2 First Term Lesson Notes Week 10

Subject: Basic Technology
Class: JSS 2
Term: First Term
Week: 10
Age: 12 years
Topic: Triangles
Sub-topic: Construction of Various Types of Triangles, Circumscribing, Inscribing, and Escribing Circles to a Given Triangle
Duration: 40 minutes

Behavioural Objectives:

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

1. Construct various types of triangles accurately.
2. Understand and perform the circumcircle, incircle, and escribed circle constructions for a triangle.

Keywords:

• Triangle: A three-sided polygon.
• Circumscribed Circle: A circle that passes through all vertices of a triangle.
• Inscribed Circle: A circle that touches all sides of a triangle.
• Escribed Circle: A circle outside a triangle, touching one side and extending to the other two.

Set Induction:

The teacher discusses the importance of triangles in geometry and architecture, asking students to recall previous lessons about triangle properties.

Entry Behaviour:

Students should have prior knowledge of triangle types and basic geometric constructions.

Learning Resources and Materials:

• Compass
• Ruler
• Protractor
• Pencil
• Sketching paper
• Triangle models

Building Background/Connection to Prior Knowledge:

Students have learned about the properties and types of triangles, which provides a basis for understanding circle constructions.

Embedded Core Skills:

• Practical skills in geometric construction
• Problem-solving skills
• Collaborative skills through group work

Learning Materials:

• Geometry textbooks
• Reference books on constructions

Reference Books:

• Lagos State Scheme of Work
• Basic Technology for Junior Secondary Schools by NERDC

Instructional Materials:

• Whiteboard and markers
• Visual aids for circle constructions

Content:

I. Construction of Various Types of Triangles

1. Equilateral Triangle:
   • Measure and draw a line segment.
   • Use a compass to draw arcs from both endpoints, intersecting to form equal angles.
2. Isosceles Triangle:
   • Draw the base.
   • Use a compass to find the apex point, maintaining equal lengths from both ends.
3. Scalene Triangle:
   • Measure three different sides.
   • Connect the points to form a triangle.

II. Circumscribing, Inscribing, and Escribing Circles

1. Circumscribed Circle:
   • Construct the perpendicular bisectors of two sides.
   • The intersection point is the center of the circumcircle.
   • Use the compass to draw the circle through the triangle’s vertices.
2. Inscribed Circle:
   • Construct the angle bisectors of the triangle.
   • The intersection point is the center of the incircle.
   • Use the compass to draw the circle touching all sides.
3. Escribed Circle:
   • Construct the angle bisector of one angle.
   • Extend the bisector to find the intersection with the opposite side.
   • Use the compass to draw the circle touching the extended side and opposite angles.

15 Fill-in-the-Blank Questions:

1. A triangle has ______ sides.
   a) Four
   b) Three
   c) Two
   d) Five
2. An equilateral triangle has ______ equal sides.
   a) No
   b) One
   c) Two
   d) Three
3. The circumcircle of a triangle passes through all its ______.
   a) Sides
   b) Angles
   c) Vertices
   d) Edges
4. The inscribed circle touches all the ______ of a triangle.
   a) Angles
   b) Vertices
   c) Sides
   d) Bisectors
5. An isosceles triangle has ______ equal sides.
   a) No
   b) One
   c) Two
   d) Three
6. The center of the inscribed circle is found at the intersection of ______.
   a) Perpendicular bisectors
   b) Angle bisectors
   c) Medians
   d) Altitudes
7. The escribed circle is located ______ a triangle.
   a) Inside
   b) Outside
   c) Above
   d) Below
8. To construct a circumcircle, you need the ______ of two sides.
   a) Midpoints
   b) Lengths
   c) Angles
   d) Bisectors
9. A scalene triangle has ______ equal sides.
   a) One
   b) Two
   c) Three
   d) No
10. The ______ triangle has one angle measuring 90°.
    a) Equilateral
    b) Right
    c) Acute
    d) Obtuse
11. The center of the circumcircle is called the ______.
    a) Centroid
    b) Circumcenter
    c) Incenter
    d) Excenter
12. The sides of the triangle are connected at the ______.
    a) Base
    b) Vertex
    c) Height
    d) Angle
13. To construct an equilateral triangle, all sides must be ______.
    a) Different
    b) Equal
    c) Short
    d) Long
14. The inscribed circle is also called the ______ circle.
    a) Excircle
    b) Circumcircle
    c) Incircle
    d) Polygon
15. A triangle can be drawn using a ______ and a ruler.
    a) Protractor
    b) Compass
    c) Marker
    d) Pencil

15 FAQs with Answers:

1. What is a triangle?
   A triangle is a three-sided polygon.
2. How do you construct an equilateral triangle?
   Draw a line segment and use a compass to create arcs from both endpoints.
3. What is the circumcircle of a triangle?
   It’s a circle that passes through all three vertices of the triangle.
4. What is an inscribed circle?
   It’s a circle that touches all sides of the triangle.
5. What is the escribed circle?
   It’s a circle outside the triangle that touches one side and the extensions of the other two.
6. How do you find the center of an inscribed circle?
   Construct the angle bisectors and find their intersection.
7. Can a triangle have two equal angles?
   Yes, it would be classified as an isosceles triangle.
8. What type of triangle has all sides different?
   It’s called a scalene triangle.
9. What tools do you need for constructing circles around triangles?
   A compass, ruler, and pencil.
10. Why are circumcircles important?
    They help in various geometric calculations and constructions.
11. How do you draw a circumcircle?
    Find the circumcenter by constructing perpendicular bisectors and draw a circle through the vertices.
12. What is the significance of the triangle’s centroid?
    It’s the point where the three medians intersect.
13. How do you measure angles in a triangle?
    Use a protractor to measure each angle.
14. What are the parts of a triangle?
    The vertices, sides, and angles.
15. What do you need to ensure while drawing triangles?
    Accuracy in measuring sides and angles.

Presentation Steps:

Step 1:

The teacher revises the previous topic about triangles and their properties.

Step 2:

The teacher introduces the new topic by explaining how to construct various types of triangles and circles associated with them.

Step 3:

The teacher allows pupils to contribute, discussing their experiences with geometric constructions and correcting them where necessary.

Teacher’s Activities:

• Demonstrate triangle constructions and circle constructions.
• Monitor students as they practice and provide guidance.
• Discuss real-life applications of triangles and circles in design.

Learners’ Activities:

• Practice constructing different types of triangles and their associated circles.
• Collaborate in pairs to share techniques and results.
• Label the parts of their sketches.

Assessment:

1. Define a triangle.
2. List the types of triangles based on sides.
3. How do you construct a circumcircle?
4. Explain the characteristics of an inscribed circle.
5. What is the process for creating an escribed circle?
6. Identify the parts of a triangle.
7. Describe a scalene triangle.
8. What is the sum of angles in a triangle?
9. How many sides does a triangle have?
10. Why are triangles important in design and construction?

Conclusion:

The teacher goes around to mark students’ work and provide feedback on their understanding of triangle constructions and circle placements.

More Useful Links

• First Term Mid Term Test Basic Technology JSS 2 First Term Lesson Notes Week 7
• Geometric Construction Circles Basic Technology JSS 2 First Term Lesson Notes Week 11
• First Term Review Assessment Questions Basic Technology JSS 2 First Term Examination Week 12