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Types Of Triangles By Sides And Angles

There are 7 types of triangles that are classified by angles and sides. Learn how to distinguish them easily.
Triangles are classified depending on their sides and angles
 

One of the first lessons in geometry at school was to learn the names of the different kind of triangles that exist, depending on their sides or on the degrees of its angles. 

However, as the years go by, this type of basic notions are forgotten, or concepts are mixed due to the lack of practice or application of it in real life. This is why today we are going back to our times at school, and we will review the types of triangles and their outstanding characteristics.

What is a triangle?

Before explaining the different types of triangles, we should refresh our memory and define what a triangle is.

The triangle is the plane polygon with fewer sides that we can find in geometry, three in total. Therefore, its vertices and internal angles will also be three. The angles all together add up to 180º, a straight line if we open up the figure. 

A triangle has the following parts:

Vertices

These are the three points that give shape to the polygon, something that when represented we use the capital letters A, B, and C.

Height

The height of the triangle is the distance from any of its sides with respect to the opposite vertex.

Base

It refers to any of the three sides of the triangle.

Sides

The sides are the sections that join two correlative vertices in a polygon. As we said, all types of triangles have three sides, and they are classified depending on their length.

How do we classify triangles?

We can classify triangles depending on the length of its sides or on its angles. 

If we focus on the sides, the types of triangles are: equilateral, isosceles and scalene; while regarding its angles, they are: right, acute, obtuse, and equiangular.

Types of triangles by sides

This is the classification of the triangles depending on its sides:

1. Equilateral triangle

The three sides of this type of triangle are the same length, so its internal angles will be the same as well (60º the three of them, 180º in total). To calculate the area of this triangle we have to take the square root of 3, divide it by 4 and multiply by the length of the side squared.

2. Isosceles triangle

The isosceles triangle has two sides the same and one shorter, so two of its angles will also have the same degrees.

3. Scalene triangle

Last, but not least, the scalene triangle has none of its sides the same, they all have different lengths; so its angles will also differ between them.

Types of triangles by sides

 

Types of triangles by angles

Another consideration when it comes to classifying the types of triangles is its internal angles:

1. Right triangle

One of the angles of a right triangle is right, ergo it measures 90º.

The sides of this type of triangles are called:

  • Cathetus: the shorter sides of the triangle; the two of them constitute the right angle.
  • Hypotenuse: the side that is opposite the right angle. By its nature, it is the longest side in a right triangle.

If we want to calculate the area of the right triangle, we have to multiply the length of the two catheti that constitute the right angle and divide it by two.

2. Acute triangle

The particularity of this type of triangle is that none of its three angles reaches 90º.

3. Obtuse triangle

This type of triangle has two acute angles (less than 90º) and an angle that is bigger than 90º but inferior than 180º.

4. Equiangular triangle

This is another name for the equilateral triangle if we look at its angles instead of the length of its sides. Since all sides are equal, their three internal angles will also be the same, 60º.

If we hypothetically unfolded this triangle in the plane, we would see that the sum of its three angles adds up to 180º, that is, a straight line.

Types of triangles by angles

 

Why is it useful to know the types of triangles?

"But why do we have to know all this? Is it useful to know what the different types of triangles are?" These are some questions about whether the lessons in geometry class would have any kind of application in real life or not.

However, geometry knowledge (in which we include knowing how to distinguish the types of triangles by sides and angles) is useful for disciplines such as technical drawing, for the planning of a building and its subsequent construction, and even for a booming market such as 3D printing.

Without going any further, physicists agree that, thanks to their shape, triangles have a greater firmness compared to other types of figures; an advantage that is used in architecture and engineering for the design of structures that have to bear a lot of weight: roads, roofs, viaducts or overpasses, among others.

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