Exploring Geometric Shapes: A Practical Journey

Objectives

1. Classify polygons according to their sides (triangles and quadrilaterals).

2. Identify the different types of triangles based on their sides and angles.

3. Recognize equilateral, equiangular, and regular polygons.

Contextualization

Polygons are present in various situations in our daily lives. From the structure of the buildings we inhabit to the complex designs of bridges and vehicles, the classification of geometric shapes is an essential skill. Understanding how to identify and categorize these shapes not only helps in mathematics but is also crucial for various professions such as architecture, civil engineering, and graphic design. For example, triangles are often used in structures due to their rigidity and stability. Quadrilaterals appear in various forms, such as in windows and doors.

Relevance of the Theme

The classification of geometric shapes is fundamental in many areas of science and engineering. In the current context, with the advancement of technology and the growing demand for safe and efficient constructions, understanding the geometry of polygons allows for the creation of more resilient and functional structures. Additionally, this skill is highly valued in the job market, especially in fields like architecture, engineering, and design.

Classification of Triangles by Sides

Triangles can be classified by their sides into three categories: equilateral, isosceles, and scalene. An equilateral triangle has all its sides equal, an isosceles triangle has two equal sides, and a scalene triangle has all sides different.

• Equilateral Triangle: All sides are equal.

• Isosceles Triangle: Two sides are equal.

• Scalene Triangle: All sides are different.

Classification of Triangles by Angles

Triangles can also be classified according to the measure of their angles: acute, right, and obtuse. An acute triangle has all angles less than 90 degrees, a right triangle has one angle of 90 degrees, and an obtuse triangle has one angle greater than 90 degrees.

• Acute Triangle: All angles are less than 90°.

• Right Triangle: Has an angle of 90°.

• Obtuse Triangle: Has an angle greater than 90°.

Classification of Quadrilaterals

Quadrilaterals are polygons with four sides and can be classified in various forms, such as: square, rectangle, rhombus, parallelogram, and trapezoid. Each of these types has specific characteristics regarding their sides and angles.

• Square: All sides and angles are equal.

• Rectangle: Opposite sides are equal and angles are right.

• Rhombus: All sides are equal, but angles are not right.

• Parallelogram: Opposite sides are equal and opposite angles are equal.

• Trapezoid: Has at least one pair of parallel sides.

Equilateral, Equiangular and Regular Polygons

Polygons can be classified according to their sides and angles. Equilateral polygons have all sides equal, equiangular polygons have all angles equal, and regular polygons have both all sides and all angles equal.

• Equilateral: All sides are equal.

• Equiangular: All angles are equal.

• Regular: All sides and angles are equal.

Practical Applications

• Architecture: Use of triangles in roof structures to increase stability.
• Civil Engineering: Designing bridges using polygons to distribute weight effectively.
• Graphic Design: Creating logos and geometric patterns using regular polygons and their aesthetic properties.

Key Terms

• Polygon: Closed geometric figure formed by line segments.

• Equilateral Triangle: Triangle with all sides equal.

• Isosceles Triangle: Triangle with two sides equal.

• Scalene Triangle: Triangle with all sides different.

• Acute Triangle: Triangle with all angles less than 90°.

• Right Triangle: Triangle with one angle of 90°.

• Obtuse Triangle: Triangle with one angle greater than 90°.

• Square: Quadrilateral with all sides and angles equal.

• Rectangle: Quadrilateral with opposite sides equal and angles right.

• Rhombus: Quadrilateral with all sides equal, but angles not right.

• Parallelogram: Quadrilateral with opposite sides equal and opposite angles equal.

• Trapezoid: Quadrilateral with at least one pair of parallel sides.

• Equilateral: Polygon with all sides equal.

• Equiangular: Polygon with all angles equal.

• Regular Polygon: Polygon with all sides and angles equal.

Questions

• How can the classification of polygons influence the stability and functionality of a construction?

• In what ways can knowledge about polygons be useful in professions such as architecture and engineering?

• What difficulties did you encounter in classifying the polygons, and how did you overcome them?

Conclusion

To Reflect

In this lesson, we explored the importance of classifying polygons and their practical applications in various professional fields such as architecture, engineering, and graphic design. Understanding the classification of triangles and quadrilaterals, as well as the identification of equilateral, equiangular, and regular polygons, allows us to apply this knowledge in real contexts, creating more resilient and aesthetically pleasing structures. The practical activities carried out provided a hands-on experience, where theory connected directly with practice, facilitating the internalization of geometric concepts.

Mini Challenge - Innovative Polygons Challenge

In this mini-challenge, you will be challenged to apply the knowledge acquired to create an innovative project using polygons.

• Form pairs or groups of three.
• Use paper and pens to draw an innovative object or structure that uses at least three different types of polygons (triangles and quadrilaterals).
• Classify each polygon used in your drawing according to sides and angles.
• Explain how the choice of polygons influenced the stability and functionality of your project.
• Present your project to the class, highlighting the classifications of the polygons and their practical applications.