The three interior angles of an acute triangle are acute.
The first thing we are going to do in order to fully enter into establishing the meaning of the term acute triangle is to know the etymological origin of the two words that give it shape:
-Triangle derives from Latin and is the result of the sum of two very different parts: the prefix «tri-«, which is synonymous with «three», and the noun «angulus», which is equivalent to «corner».
-Acutangulo, on the other hand, we can also say that it comes from Latin. In his case it is the result of the union of "acutus", which can be translated as "acute", and "angulus", which is synonymous with "corner" or " angle ".
A polygon is a plane figure bounded by a certain number of segments, which are called sides . When the polygon has three sides , it is called a triangle .
Characteristics of an acute triangle
According to their characteristics, it is possible to distinguish between several types of triangles. Acute triangles are those whose three interior angles are acute , since they measure less than 90º .
This means that a triangle whose interior angles measure 45º , 80º and 55º , for example, is an acute triangle: its three angles are acute. If it had an angle that measures 90º , however, it would be a right triangle due to the presence of the right angle . On the other hand, if one of its angles were obtuse (more than 90º ), it would be classified as an obtuse triangle .
It is important to note that acute triangles and obtuse triangles are also part of the group of oblique triangles , a name that refers to the fact that none of the internal angles are right.
Acute triangles are also oblique.
The measurements of the sides
If we focus on the measurements of their sides, acute triangles can also be included in other sets. There are acute triangles that are also equilateral triangles because their three sides measure the same. Other acute triangles are isosceles triangles , with two identical sides and one different side. Acute triangles, finally, can be scalene triangles if the three sides have different extensions.
Taking into account what has been explained, it is important to remember that a triangle can be acute and equilateral or acute and scalene, to name two possibilities, since they are classifications that refer to different characteristics of the figures.
Other characteristics of the acute triangle
In addition to everything stated above, we cannot ignore that this type of triangle that concerns us comes to strictly comply with the set of singularities and characteristics that are attributed to triangles in general:
-The sum of two of its sides becomes greater than the length of the third side.
-In the acute triangle it is evident, because what is known as the sine theorem is fulfilled.
-If two midpoints of two of the sides of the aforementioned triangle were joined, a segment would be shaped that would be parallel to the third side. And that parallel, in turn, we can determine that it would have a length that would be half of the other.
-The sum of its internal angles adds up to 180º.