# Types of triangles

Everyone in our lives has heard about or studied about **triangles** . Within the **mathematical** sciences , **geometry** is studied , this branch involves the study of **geometric figures** , where triangles are included.

Geometry is a very useful knowledge for several reasons, among them it is the fundamental basis for technical drawings, planning of works and constructions.

It is always good to refresh knowledge acquired in the past or learn new things.

In this article we will see the different types of triangles and their characteristics.

Triangle type | Characteristic |

Equilateral | All its sides and angles are equal |

Isosceles | They have equal sides and a different one |

Scalenes | All its sides are different |

Rectangle | They have a right angle of 90 degrees. |

Acute angle | All of its angles are acute. |

Obtuse angle | It has an obtuse angle. |

Index

## What is a triangle?

When we speak of a **triangle** we speak of a polygon. It is a flat geometric figure that has area but no volume.

All triangles share certain **characteristics** , which we detail below:

- All triangles have three
**sides** - All triangles have three
**vertices** - All triangles have three interior
**angles**and the sum of them gives us 180 degrees. - A triangle cannot have more than one right or obtuse angle.
- Either side of a triangle is always less than the sum of the other two sides, but greater than their difference.

When we speak of vertex, it refers to each of the points that determine a triangle. They are usually marked with capital letters.

The base of the triangles can be any of their sides, the one that is opposite to the vertex.

The height of the triangles is the distance a side has from its opposite vertex.

The sides as indicated are always three, but they vary in their sizes and that is what generates the classification of the different types of triangles.

#### How do you find the area of a triangle and its perimeter?

The **perimeter** and the **area** are two fundamental measurements that we need to know and calculate of a triangle. Let’s see how they are calculated:

To calculate the perimeter, the lengths of all its sides must be added.

To calculate the area of the geometric figure, the following formula should be applied: base times height and then divide this result in two.

## Types of triangles

Based on the classification of triangles according to their sides, we can find three different types:

- Equilateral triangles
- Isosceles triangles
- Scalene triangles

#### Equilateral

They are defined as equilateral to those triangles that have all their sides of equal length, which means that it is a regular polygon. Their angles are also equal, each measuring 60 degrees.

#### Isosceles

These triangles have the characteristic of having two equal sides and two equal angles.

#### Scalenes

These types of triangles have all their different sides, that is, the length of each of their sides is different.

Another type of classification that can be given to triangles is according to their **angles** :

- Right triangles
- Acute triangles
- Obtuse triangles

#### Rectangles

This classification includes those triangles that have a right angle, that is, ninety degrees. The side opposite the right angle is called the hypotenuse and the other two are called the legs.

The hypotenuse will always be larger than any of its legs. In this type of triangle the two acute angles are complementary and add up to 90 degrees.

#### Acute angles

Acute triangles are those that have the three acute angles, that is, with less than 90 degrees.

#### Obtuse angles

They are those triangles in which all their internal angles are obtuse, that is, greater than 90 degrees.

## Angles

To understand triangles well, we must be clear about the concept of **angle** . An angle is called the part of the plane or portion that separates two lines that have the same point in common. It is also considered as an angle to the rotation that one of its sides should make to move from one position to the other.

An angle is made up of different elements, among them: **lines** that are related and **vertex** or point of union between said lines.

There are different types of angles that will give rise to the different geometric figures, including the triangles that we have detailed previously.

**Acute angle** : are those that measure between zero and ninety degrees, without reaching the latter.

**Right angle:** one that measures exactly ninety degrees. For example, the sides of a square form a right angle.

**Obtuse angle** : those angles that measure between 90 and 180 degrees, without reaching the latter, bear this name.

**Flat angle:** represents that angle whose measurement is 180 degrees. The straight lines that make up the figure are joined in such a way that it seems that one continues the other, as if they were a single line.

**Concave angle:** refers to that angle whose measurement ranges between 180 degrees and 360 degrees. To realize this, let’s take an example of a cake, the concave angle is the one that would form what remains of the cake as long as we did not eat more than half.

**Complete or perigonal** angle **:** said angle completes 360 degrees, in which the object that performs it remains in its original position. If we make a complete turn we will be in the same position as the initial one.

**Null angle:** corresponds to those that measure 0 degrees.

## Trigonometric functions

**Trigonometric functions** are called the functions of an angle. The functions or ratios between the angles of a right triangle are the relationships between the **legs** and the **hypotenuse.**

Over any acute angle of a right triangle we will have:

**Sine:**abbreviated as sin, it is the ratio or division of the length of the opposite leg and the length of the hypotenuse.**Cosine**: abbreviated cos, reference to the division between the length of the adjacent leg and the length of the hypotenuse.**Tangent:**abbreviated tan, reference to the division between the length of the opposite leg and the adjacent leg. That is to say to the division between the sine and the cosine.

## Theorems based on right triangles

Among the most important theorems about triangles we find:

### Pythagorean theorem

This theorem allows us to relate the three sides of a right triangle. It is very useful when we know two of its sides and we want to find out the third, by means of this equation we can obtain the result.

As we have explained, the right triangle is one in which one of its sides has an angle of 90 degrees. On this side the name of hypotenuse is attributed and the other two the name of leg.

This theorem says that: in every right triangle the square of the hypotenuse is equal to the sum of the squares of the legs. That is, I feel c the hypotenuse and a and b the legs then:

Thanks to this theorem, the value of one of the legs can be found, knowing the value of the other leg and the hypotenuse.

### Height theorem

This theorem relates the height of a triangle and the legs of two triangles similar to the main one, by plotting the height above the hypotenuse. That is, in every right triangle the height relative to the hypotenuse is the geometric mean of two projections of the legs on the hypotenuse.

### Catheter theorem

This theorem relates the projected segments of the legs on the hypotenuse with each of the legs, that is: in every right triangle, a leg is the geometric mean between the hypotenuse and the projection of that leg on it.

Divide the triangle by its height into two smaller triangles.