# The 7 types of triangles: classification according to their sides and angles

September 3, 2022

During our childhood, we all had to attend math classes at school, where we had to study the different types of triangles. However, over the years we can forget about some things we have studied. For some individuals, mathematics is a fascinating world, but others enjoy more with the world of letters.

In this article we will review the different types of triangles , so it can be useful to refresh some concepts studied in the past or to learn new things that were not known.

• Recommended article: "The 7 types of angles, and how they can create geometric figures"

## Usefulness of triangles

In mathematics, geometry is studied, and different geometrical figures such as triangles are deepened. This knowledge is useful for many reasons; for example: to make technical drawings or to plan a work and its construction.

In this sense, and unlike a rectangle that can be transformed into a parallelogram when force is applied to one of its sides, the sides of a triangle are fixed. Due to the rigidity of their forms, physicists demonstrated that the triangle can withstand high amounts of force without deforming. Therefore, architects and engineers use triangles when building bridges, roofs in houses, and other structures. When constructing triangles in structures, the resistance increases when reducing lateral movement .

## What is a triangle

The triangle is a polygon, a flat geometric figure that has area but not volume. all triangles have three sides, three vertices and three internal angles, and the sum of these is 180º

The triangle consists of:

• Vertex : each of the points that determines a triangle and that are usually indicated by uppercase Latin letters A, B, C.
• Base : it can be any of its sides, the opposite of the vertex.
• Height : is the distance from one side to its opposite vertex.
• Sides : they are three and because of these, triangles are usually classified in different ways.

In these figures, one side of this figure is always smaller than the sum of the other two sides, and in a triangle with equal sides, their opposite angles are also equal.

## How to calculate the perimeter and area of ​​a triangle

Two measures that interest us to know about the triangles are the perimeter and the area. To calculate the first, it is necessary to add the lengths of all its sides:

P = a + b + c

On the other hand, to know what the area of ​​this figure is, the following formula is used:

A = ½ (b h)

Therefore, the area of ​​the triangle is base (b) by height (h) divided by two, and the result value of this equation is expressed in square units.

## How triangles are classified

There are different types of triangles, and they are classified taking into account their side lengths and the amplitude of their angles . Considering its sides, there are three types: equilateral, isosceles and scalene. Depending on their angles, we can distinguish right triangles, obtusángulos, acutángulos and equiangles.

Then we go to detail them.

## Triangles according to the length of their sides

Considering the length of the sides, the triangles can be of different types.

### 1. Equilateral triangle

An equilateral triangle has three sides of equal length, so it is a regular polygon . The angles in an equilateral triangle are also equal (60º each). The area of ​​this type of triangle is the root of 3 between 4 times the length of the side squared. The perimeter is the product of the length of one side (l) by three (P = 3 l)

### 2. Scalenic triangle

A scalene triangle has three sides of different lengths , and their angles also have different measurements. The perimeter is equal to the sum of the lengths of its three sides. That is: P = a + b + c.

### 3. Isosceles triangle

An isosceles triangle has two sides and two equal angles , and the way to calculate its perimeter is: P = 2 l + b.

## Triangles according to their angles

Triangles can also be classified according to the amplitude of their angles.

### 4. Right triangle

They are characterized by having a straight interior angle, with a value of 90º . The legs are the sides that make up this angle, while the hypotenuse corresponds to the opposite side. The area of ​​this triangle is the product of its legs split between two. That is: A = ½ (bc).

### 5. Obtuse triangle

This type of triangle has an angle greater than 90 ° but less than 180 ° which is called "obtuse" , and two acute angles, which are less than 90 °.

### 6. Acute angle triangle

This type of triangle is characterized because it has its three angles that are less than 90 °

### 7. Equiangular triangle

It is the equilateral triangle, since its internal angles are equal to 60 °.

### conclusion

Practically all of us have studied geometry in school, and we are familiar with triangles . But over the years, many people may forget what their characteristics are and how they are classified. As you have seen in this article, triangles are classified in different ways depending on the length of their sides and the amplitude of their angles.

Geometry is a subject that is studied in the subject of mathematics, but not all children enjoy this subject. In fact, some have serious difficulties. What are the causes of this? In our article "Children's difficulties in learning mathematics" we explain it to you.

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