Context

Hello, class! Today we are going on an incredible mathematical adventure. Did you know that triangles are everywhere? Yes, they are geometric figures formed by three line segments that meet. Look around the room, can you find any triangles?

Triangles are very important in our daily lives. They are present in simple things like the tip of a pen, the letter A, the roof of a house, the candles on a cake, and even in the posters we use for studying. But did you know that each triangle has unique characteristics that make it special?

Introduction

In this project, we will explore the Components of Triangles. But what are these components? Well, class, the components of a triangle are the parts that form it and the properties it possesses. Let's learn about three essential components: sides, angles, and height.

First, the sides of a triangle. They are the line segments that join the vertices of the triangle. A triangle can have three equal sides, we call this an equilateral triangle. It can have two equal sides, we call it an isosceles triangle. Or it can have all different sides, we call it a scalene triangle.

Now, the angles. They are the openings formed by the sides of a triangle. A triangle can have three equal angles, we call this an equiangular triangle. It can have an angle greater than 90°, we call it an obtuse triangle. Or it can have an angle less than 90°, we call it an acute triangle.

Finally, the height of the triangle. It is the line segment that starts from a vertex of the triangle and is perpendicular to the side opposite this vertex. The height is very important for calculating the area of the triangle.

Now that we know the basics, are you ready to embark on this adventure? Let's go!

Practical Activity: Exploring the Components of Triangles

Project Objective

The objective of this project is for you, in groups, to build triangles using various materials, identify their properties, and present to the class what you have discovered. This way, you will learn in practice about the components of triangles and how they relate to each other.

Project Description

Each group should create, at least, three triangles of different sizes and shapes. You can use straws, toothpicks, modeling clay, wire, paper, or any other safe and available material. Then, you should measure the sides and angles of each triangle and write down the measurements. Finally, using a pencil and a ruler, you should draw the height of each triangle and measure the obtained value.

Required Materials

• Straws, toothpicks, modeling clay, wire, paper, or any other safe and available material for building the triangles;
• Ruler;
• Pencil;
• Protractor;
• Tape measure or ruler with centimeter markings.

Step by Step

1. Form groups of 3 to 5 students.
2. With the available materials, build the triangles. Remember to vary their size and shape.
3. Using the ruler, measure the sides of each triangle. Write down the measurements.
4. With the protractor, measure the angles of each triangle. Write down the measurements.
5. Using the pencil and ruler, draw the height of each triangle. Measure the obtained height.
6. With the collected measurements, identify if any triangle is equilateral, isosceles, or scalene; equiangular, obtuse, or acute.
7. Prepare a presentation for the class showing the triangles you built, talking about their measurements, and explaining which ones are equilateral, isosceles, or scalene, and equiangular, obtuse, or acute. Don't forget to talk about the heights too!

Delivery Format

The project presentation should be done orally, with the exhibition of the built triangles and explanations about the components of each one. In addition, each group should deliver a report containing the collected measurements and the classifications of the triangles. The report can be done on a sheet of paper, with drawings and legible writing.

Remember, collaboration, creativity, and respect within the group and with other classmates are very important. Have fun, mathematical adventurers!