Elements of a triangle- for children (with solved exercises!)

The elements of a triangle are three sides, three vertices and three angles. And in this new lesson from a Teacher we will see what are the elements of a triangle in a deeper way so that you can better understand this concept of geometry. We will start with its definition and properties and then finish with its elements. Then we'll do some exercises with solutions to consolidate what has been learned.

Index

1. What is a triangle?
2. What are the elements of a triangle
3. triangle properties
4. types of triangles
5. Triangle exercises with solutions

Before beginning to know the elements of a triangle, we will better understand what geometric figure we are dealing with. The triangles or also called trines are those flat geometric figures that have three sides that are in contact with each other. The common points that join them are called vertices. The name attributed to these basic flat figures is due to the fact that they have

In history, humanity has studied triangles since ancient times as they are associated with divinity and magic. In ancient Greece, Pythagoras was the one who made the Theorem of him, called Pythagoras theorem precisely by its creator, where he established that the square of the hypotenuse is equal to the sum of the square of the legs of a right triangle.

A feature of the right triangles is that one of its sides is longer, and is called the hypotenuse, while the other two are shorter and are called legs. The legs are the sides that form the right angle.

Triangles can be classified into different types, depending on the shape of the sides and the angles they have. Despite this, we can say that they always have three sides and the interior angles always add up to 180° sexagesimals. In unProfesor we leave you a lesson about classification of triangles.

Triangles are made up of several elements. As we studied earlier, they have three sides, three vertices, and three angles. Let's see what are the elements of a triangle.

sides

They are the straight lines that form the triangle, and that join the vertices of it. These lines delimit the figure. Triangles always have only three sides.

vertices

They are the points that define the triangles. They are formed from joining two lines at this point. Triangles always have only three vertices.

angles

Two sides of a triangle form an angle at the common vertex between them. This angle is called the interior angle of the triangle, since it is formed inside the polygon. Like sides and vertices, triangles have only three interior angles.

Once the elements of a triangle are known, we are going to see its properties. As we saw previously, they are basic flat geometric figures that have three sides that form it. That is, they are polygons formed by three sides, three angles and three vertices.

• The sum of all interior angles of any triangle always add exactly 180° sexagesimals. This property is called the sum of angles of a triangle.
• The sum of all exterior angles of any triangle always adds exactly 360° sexagesimals.
• The sum of the lengths of two sides of a triangle is always greater than the length of the remaining side.
• An exterior angle of a triangle is equal to the sum of the two opposite interior angles.
• Triangles are the only polygons that They do not have diagonals.
• All polygons, other than triangles, can be divided into triangles. That is, a hexagon can be divided into triangles, an octagon can also be divided into triangles, just like a square and a rectangle.
• At least two angles of a triangle they are sharp.

There are different types of triangles according to their sidesand their angles. Let's see their classification.

according to their sides

It depends on the relationship that exists between its three sides, the triangles can be:

• equilateral: when the three sides have the same length, that is, they measure exactly the same.
• Isosceles: when two of its sides have the same length but the third has a different measure than the other two.
• Scalene: when none of its three sides have the same length.

according to their angles

It depends on the opening of the angles that form its sides, the triangles can be:

• rectangles: one of its interior angles measures 90° sexagesimals and is formed by the two legs opposite the longest of its sides called the hypotenuse.
• oblique: are the triangles that do not have any of their right angles. They can be obtuse or acute. Obtuse triangles are those in which one of its interior angles is obtuse, that is, greater than 90° sexagesimal, and its other two angles are acute, or less than 90°. While acute triangles are those whose three interior angles are less than 90° sexagesimal.

Different triangles can be formed with these combined classifications, that is, there are triangles that have two classifications together, such as isosceles right triangles, acute triangles scalenes, etc.

Which is the correct option taking into account what has been learned in this lesson from a Teacher.

Exercise 1

What is obtained by cutting a square along its diagonal?

• Two equilateral right triangles
• Two isosceles right triangles
• Two equilateral acute triangles

Solution

Two isosceles right triangles. The legs measure the same because they are part of a square, but the hypotenuse, being the diagonal, has a greater length.

Exercise 2

According to the sides, an obtuse triangle...

• can never be equilateral
• can never be isosceles
• Both of the above statements are correct.

Solution

It can never be equilateral. Equilateral triangles always have their interior angles of 60° sexagesimal, so none of their angles can be obtuse.

Exercise 3

In an equilateral triangle...

• The longer the sides, the larger the interior angles.
• The smaller the sides, the smaller the interior angles.
• None of the above statements is correct

Solution

None of the statements are correct, since its angles will always measure 60° sexagesimal regardless of the size of its sides.

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If you want to read more articles similar to elements of a triangle, we recommend that you enter our category of Geometry.

• Quishpe Vaca, J. m. (2018). Study of triangles (Master's thesis, National University of Education).
• Joya Cetina, C. A., & Suárez Sotomonte, P. (2020). Discovery learning in systems of points and notable lines of the triangle. Praxis & Knowledge, 11(26).
• Rey, M., Tapia, L., Hernández, C., & Tarifa, H. (2010). Didactic sequence for teaching triangles.