Lesson Plan | Traditional Methodology | Triangles: Classification by Sides

Objectives

Duration: 10 to 15 minutes

The purpose of this stage of the lesson plan is to provide a clear and detailed understanding of the main objectives that students should achieve by the end of the lesson. These objectives will guide the teaching and learning process, ensuring that students acquire essential skills to classify triangles based on their sides and verify the conditions for the existence of a triangle.

Main Objectives

1. Classify triangles based on their sides as equilateral, isosceles, or scalene.

2. Verify the conditions for the existence of a triangle.

Introduction

Duration: 10 to 15 minutes

The purpose of this stage of the lesson plan is to contextualize students about the importance of triangles and motivate them to learn about their classification. By understanding the relevance of triangles in the real world, students become more engaged and interested in the content that will be covered. This introduction prepares the ground for a more detailed and technical explanation about the classification of triangles based on their sides.

Context

To begin, explain to the students that triangles are fundamental geometric shapes that appear in various areas of mathematics and everyday life. A triangle is a flat figure formed by three line segments that meet at three distinct points called vertices. They are important not only in mathematics but also in engineering, architecture, and many other disciplines. Understanding the different types of triangles is essential for solving more complex problems and for the practical application of geometric knowledge.

Curiosities

🧐 Did you know that the triangular shape is one of the most stable in civil construction? This is because a triangle, unlike other geometric shapes, does not deform when a force is applied. Therefore, many structures, like bridges and roofs, use triangles in their construction to ensure greater stability and resistance.

Development

Duration: 40 to 45 minutes

The purpose of this stage of the lesson plan is to provide a detailed and organized explanation of the classification of triangles based on their sides and the conditions necessary for the existence of a triangle. This stage is crucial for consolidating students' theoretical knowledge, allowing them to recognize and correctly apply the concepts learned in practical situations and mathematical problems.

Covered Topics

1. Classification of Triangles Based on Sides: Explain that triangles can be classified into three main types based on the lengths of their sides: equilateral, isosceles, and scalene. 2. Equilateral Triangle: Detail that an equilateral triangle has all three sides equal and, consequently, all three internal angles are also equal, measuring 60 degrees each. 3. Isosceles Triangle: Explain that an isosceles triangle has two equal sides and one different side. The angles opposite the equal sides are also equal. 4. Scalene Triangle: Describe that a scalene triangle has all its sides of different lengths, and therefore, all its internal angles are also different. 5. Conditions for the Existence of a Triangle: Inform that for three segments to form a triangle, the sum of the lengths of any two sides must always be greater than the length of the third side.

Classroom Questions

1. Classify the triangle with side lengths of 5 cm, 5 cm, and 8 cm. 2. Check if it is possible to form a triangle with side lengths of 3 cm, 4 cm, and 5 cm. 3. Explain why it is not possible to form a triangle with side lengths of 2 cm, 2 cm, and 5 cm.

Questions Discussion

Duration: 25 to 30 minutes

The purpose of this stage of the lesson plan is to ensure that students deeply understand the concepts discussed by revisiting and analyzing the answers to the proposed questions. This moment of discussion and engagement is crucial for consolidating learning, allowing for critical reflection, and promoting a more robust and applied understanding of triangles and their properties.

Discussion

• 📝 Classification of the triangle with side lengths of 5 cm, 5 cm, and 8 cm: This is an isosceles triangle, as it has two equal sides (5 cm) and one different side (8 cm). The angles opposite the equal sides will also be equal.

• 📝 Verification of the possibility of forming a triangle with side lengths of 3 cm, 4 cm, and 5 cm: Yes, it is possible to form a triangle with these lengths. Check the conditions for existence: 3 + 4 > 5, 3 + 5 > 4, 4 + 5 > 3. All sums are greater than the third side, therefore, these segments form a scalene triangle.

• 📝 Explanation of the impossibility of forming a triangle with sides of 2 cm, 2 cm, and 5 cm: It is not possible, as it does not satisfy the condition for existence. Check: 2 + 2 is not greater than 5. Therefore, these segments cannot form a triangle.

Student Engagement

1. 🗣️ Question 1: Why does an isosceles triangle have two equal angles? What implications does this have for solving geometric problems? 2. 🗣️ Question 2: How does the condition for the existence of a triangle (the sum of two sides being greater than the third) relate to the structural stability of triangles in constructions? 3. 🗣️ Question 3: If you have a triangle with sides measuring 7 cm, 10 cm, and 5 cm, what is the classification of this triangle? Verify the conditions for existence and classify it. 4. 🗣️ Question 4: Discuss why equilateral triangles are often used in design and art. What special properties do these triangles have that make them desirable?

Conclusion

Duration: 10 to 15 minutes

The purpose of this stage of the lesson plan is to summarize and consolidate the knowledge acquired during the lesson, reinforcing key concepts and demonstrating the practical relevance of the content, ensuring that students understand the importance and application of triangles in various fields.

Summary

• Triangles can be classified based on their sides into three types: equilateral, isosceles, and scalene.
• An equilateral triangle has all sides equal and all internal angles equal (60 degrees each).
• An isosceles triangle has two equal sides and one different side, with angles opposite to the equal sides also equal.
• A scalene triangle has all sides and internal angles different.
• For three segments to form a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

The lesson connected theory with practice by presenting concrete examples of classification of triangles and checking conditions for existence, allowing students to directly apply theoretical concepts in mathematical problems and practical situations of everyday life.

The study of triangles is essential for various fields such as engineering and architecture due to their structural stability. Understanding their properties enables the resolution of complex problems and is fundamental for the construction of safe and efficient structures, as well as being applicable in design and art.