Introduction

Triangles are one of the most important and basic geometric shapes. They are made up of three sides and three angles and we can find them everywhere around us, from the pyramids of Ancient Egypt to the structures of the bridges and buildings we see today. Moreover, triangles are very important in mathematics and other fields like physics, engineering, architecture, design, etc.

There are several types of triangles, which can be classified according to their sides and angles. Triangles with all sides equal are called equilateral, with two equal sides isosceles and with all sides different, scalene. Regarding the angles, we can have right triangles, where one of the angles is 90º, acute triangles, where all angles are less than 90º and obtuse triangles, where one of the angles is greater than 90º.

However, there is much more to triangles than what meets the eye. The properties of triangles are fascinating and can unveil many mathematical mysteries. For example, the sum of the internal angles of any triangle is always 180º. It is remarkable how this property holds regardless of the type of triangle.

Contextualization

In the real world, triangles have many applications. They are used in design and architecture to create interesting shapes and stable structures. For instance, the pyramids in Egypt are formed by triangles that provide them with great stability. In civil engineering, triangles are used to build structures such as bridges and roofs. In art, triangles are used to create patterns and forms.

Furthermore, triangles are also used in several academic disciplines like physics, chemistry, biology, geography, etc. They are used for measuring distances, calculating areas and volumes, and solving problems in analytical geometry and trigonometry.

Studying triangles is an excellent way to develop mathematical and reasoning skills because the properties of triangles allow us to solve complex problems and have a better understanding of the world around us.

Hands-on Activity: "Constructing and Classifying Triangles"

Project Goal

The goal of this project is to familiarize students with the properties, classification and construction of triangles. By the end of the project, the groups of students will be able to identify the characteristics of triangles, classify them based on their sides and angles, and also explore the applicability of the concept in everyday life.

Detailed Project Description

In this activity, students will be divided into groups of 3 to 5 individuals. Each group will be responsible for constructing different types of triangles, classifying them and, also, developing a presentation about a real-life example of the application of triangles.

Required Materials

1. Card stock or poster board
2. Ruler
3. Compass
4. Scissors
5. Glue
6. Colored markers

Detailed Step by Step Instructions

1. Theoretical research: Each group should start with a theoretical research on triangles. They must understand and write down the properties, the types of triangles according to their sides and angles, and the applications of triangles in the real world.
2. Construction of the triangles: Using the poster board, the ruler, the compass and the scissors, the groups will have to build three different triangles: an equilateral, an isosceles, and a scalene, and also classify them according to the angles (right, acute and obtuse).
3. Classification of the triangles: With the triangles built, each group should use the colored markers to write down the classification of the triangles according to their sides and their angles.
4. Applied research: The groups should investigate and discuss a practical application of triangles in the real world. It could be a human construction, a natural occurrence, etc. They should prepare a presentation, which could be a poster or a digital presentation, explaining the chosen application and how triangles are used or found in it.
5. Final Report: To finish, each group should prepare a report, divided into introduction (contextualizing the importance and the applications of triangles), development (explaining the theory of triangles, the process of constructing the triangles, and the applied research), conclusion (highlighting the main learnings and takeaways of the project), and references (listing the sources consulted during the research).

Project Deliverables

The final project deliverable will consist of:

1. Constructed Triangles: The physical models of the triangles constructed and classified by the group.
2. Practical Application Presentation: A poster or digital presentation illustrating and explaining the selected practical application of triangles.
3. Final Report: A detailed report on the project experience, including the theory of triangles, the description of the construction process of the triangles, the discussion on the practical application and the group´s conclusions about the work.

This project focuses both on the theoretical and practical knowledge of triangles and also on the teamwork. It is important that the students are engaged in all the different steps and that they have a clear and efficient communication and collaboration environment in order to succeed in the realization of the tasks.