Understanding Triangles: Types, Construction, and Applications in Technical Drawing SS 1 First Term Lesson Notes Week 10

Technical Drawing, SS 1, First Term, Week 10 on Triangles.

Lesson Plan: Triangles

Subject: Technical Drawing
Class: SS 1
Term: First Term
Week: 10
Age: 14-16 years
Topic: Triangles
Sub-Topic: Construction and Classification of Triangles
Duration: 40 minutes

Behavioral Objectives

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

1. Identify the roof trusses of a building with a low ridge roof as an example of triangles in architecture.
2. Label and explain the parts of a triangle.
3. Describe various types of triangles based on angles and sides.
4. Construct different types of triangles using given measurements.
5. Differentiate between inscribed, circumscribed, and ascribed circles related to triangles.

Keywords

• Triangle
• Equilateral, isosceles, scalene
• Right, acute, obtuse
• Inscribed circle
• Circumscribed circle
• Ascribed circle

Set Induction

The teacher will begin the lesson by showing images of roof trusses and pointing out the triangular shapes found in these structures. Students will be encouraged to discuss where they see triangles in their environment.

Entry Behavior

Students are familiar with basic shapes and types of angles, which are foundational concepts for understanding triangles.

Learning Resources and Materials

• Rulers
• Compass
• Protractors
• Set squares
• Visual aids of roof trusses and architectural designs using triangles

Building Background/Connection to Prior Knowledge

Students have previously studied angles and lines, which will assist in understanding the types of triangles and their constructions.

Embedded Core Skills

• Observation and spatial awareness
• Geometric construction
• Classification and differentiation

Learning Materials

• Lagos State Scheme of Work for Technical Drawing
• Illustrated diagrams of triangles and their parts

Reference

• Lagos State Scheme of Work
• “Technical Drawing and Engineering Graphics” by A. Bankole

Instructional Materials

• Visual aids showing various types of triangles
• Drawing instruments for triangle construction

Content Outline

1. Parts of a Triangle:
   • Basic components: vertices, sides, and angles.
2. Types of Triangles:
   • By angles: right, acute, and obtuse triangles.
   • By sides: equilateral, isosceles, and scalene triangles.
3. Construction of Triangles:
   • Methods to construct different types of triangles with given measurements.
4. Inscribed, Circumscribed, and Ascribed Circles:
   • Definitions and step-by-step methods to draw inscribed, circumscribed, and ascribed circles in relation to triangles

Triangles

:

1. Identify Roof Trusses:
   • Explanation: Roof trusses are triangular frameworks commonly used in construction to support roofs. Understanding trusses helps students connect triangles to real-world structures.
   • Types of Roof Trusses:
     • King Post Truss: A simple triangular truss with a central vertical post, often used for short spans.
     • Queen Post Truss: Similar to a king post truss but with two vertical posts, suitable for longer spans.
     • Pratt Truss: Common in bridges, this truss has diagonal members that slope toward the center.
   • Why it’s Important: Recognizing these structures helps students understand how triangles provide stability and strength in engineering and architectural design.
2. Label Parts of a Triangle:
   • Explanation: Every triangle has basic parts that define its structure, and identifying these parts is foundational for geometric constructions.
   • Parts of a Triangle:
     • Vertices: The three corner points (A, B, C).
     • Sides: The three line segments connecting the vertices (AB, BC, AC).
     • Angles: The three angles formed at each vertex.
   • Why it’s Important: Labeling parts accurately is essential for clarity in technical drawings and allows students to communicate geometric information effectively.
3. Describe Types of Triangles:
   • Explanation: Triangles are classified based on side lengths and angle measures, and understanding these types helps students in constructing and identifying triangles in different contexts.
   • Types of Triangles by Sides:
     • Equilateral Triangle: All sides and angles are equal (each angle is 60°).
     • Isosceles Triangle: Two sides are equal, and two angles are equal.
     • Scalene Triangle: All sides and angles are different.
   • Types of Triangles by Angles:
     • Acute Triangle: All angles are less than 90°.
     • Right Triangle: Has one 90° angle.
     • Obtuse Triangle: Has one angle greater than 90°.
   • Why it’s Important: Classifying triangles aids in choosing the appropriate triangle type for different technical drawing purposes, such as construction and design.
4. Construct Triangles:
   • Explanation: Constructing triangles involves drawing them with specific side lengths and angles, an essential skill in geometry and technical drawing.
   • Basic Steps:
     • Draw one side to the given length.
     • Use a compass to set and draw arcs for the other sides based on the required lengths.
     • Mark the intersection of the arcs as the third vertex and connect the points.
   • Why it’s Important: Constructing triangles accurately is key for creating precise technical drawings and models used in various applications, such as floor plans and structural designs.
5. Differentiate Between Inscribed, Circumscribed, and Escribed Circles Related to Triangles:
   • Explanation: These circles are associated with triangles and involve different relationships to the triangle’s vertices and sides. Understanding them helps students analyze geometric relationships and construct specialized shapes.
   • Types of Circles Related to Triangles:
     • Inscribed Circle: A circle drawn inside a triangle, touching all three sides.
       • Use: Helps in creating patterns and calculations within the triangle.
     • Circumscribed Circle: A circle drawn around a triangle, passing through all three vertices.
       • Use: Useful in constructing symmetrical designs and analyzing polygon relationships.
     • Escribed Circle: A circle that touches one side of the triangle and the extensions of the other two sides.
       • Use: Used in advanced geometric constructions, especially in engineering and architectural contexts.
   • Why it’s Important: Differentiating these circles allows students to analyze geometric figures in more depth and apply these shapes to technical drawings and designs.

Fill-in-the-Blank Questions

1. A triangle with all three sides equal is called a(n) ______ triangle (a. isosceles, b. equilateral, c. scalene, d. right).
2. A triangle with one 90-degree angle is a(n) ______ triangle (a. right, b. acute, c. obtuse, d. isosceles).
3. An ______ triangle has all sides of different lengths (a. scalene, b. equilateral, c. isosceles, d. acute).
4. The point where the three medians of a triangle meet is called the ______ (a. centroid, b. orthocenter, c. circumcenter, d. incenter).
5. A circle that touches all sides of a triangle is called a(n) ______ circle (a. inscribed, b. circumscribed, c. ascribed, d. tangent).
6. The longest side in a right triangle is called the ______ (a. hypotenuse, b. base, c. altitude, d. median).
7. A triangle with two equal sides is called a(n) ______ triangle (a. isosceles, b. equilateral, c. scalene, d. obtuse).
8. The ______ of a triangle is the line segment drawn from a vertex perpendicular to the opposite side (a. altitude, b. median, c. angle bisector, d. base).
9. A triangle that has all angles less than 90 degrees is known as a(n) ______ triangle (a. obtuse, b. right, c. acute, d. scalene).
10. A triangle with one angle greater than 90 degrees is a(n) ______ triangle (a. obtuse, b. acute, c. right, d. isosceles).

FAQ

1. What is an equilateral triangle?
   • A triangle with all three sides of equal length.
2. What is the difference between an acute and an obtuse triangle?
   • An acute triangle has all angles less than 90 degrees, while an obtuse triangle has one angle greater than 90 degrees.
3. What is an inscribed circle in a triangle?
   • A circle drawn inside the triangle, touching all three sides.
4. What is the hypotenuse?
   • The longest side in a right triangle, opposite the right angle.
5. How is a circumscribed circle different from an inscribed circle?
   • A circumscribed circle surrounds the triangle, passing through all its vertices.

Presentation Steps

Step 1: Revision of Previous Topic
The teacher will quickly review the previous lesson on angles, focusing on their measurement and classification.

Step 2: Introduction of New Topic
The teacher will introduce triangles, showing visual aids to help students identify the types and parts of triangles.

Step 3: Student Contributions and Corrections
Students will engage in activities to measure angles and sides to construct triangles, while the teacher provides corrections as necessary.

Teacher’s Activities

• Explain the different types and properties of triangles.
• Demonstrate how to construct various types of triangles on a drawing sheet.
• Guide students in constructing inscribed, circumscribed, and ascribed circles for triangles.

Learner’s Activities

• Draw and label different types of triangles.
• Construct given triangles using specific measurements.
• Practice drawing inscribed, circumscribed, and ascribed circles in relation to triangles.

Assessment

• The teacher will assess students’ ability to correctly classify, construct, and label triangles.
• Observation of students’ ability to differentiate between inscribed, circumscribed, and ascribed circles.

Evaluation Questions

1. Name the triangle with all equal sides.
2. How would you identify an obtuse triangle?
3. Describe an inscribed circle.
4. What is the hypotenuse?
5. How does a circumscribed circle relate to a triangle?

Conclusion

The teacher will summarize the types of triangles and their applications in real-life contexts, especially in architectural structures.