The first thing we are going to do in order to fully enter into the establishment of the meaning of the term acute triangle is to know the etymological origin of the two words that shape it:
-Triangle is derived from Latin and is the result of the sum of two distinct parts: the prefix "tri-", which is synonymous with "three", and the noun "angulus", which is equivalent to "corner".
-Acutgulo, 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 flat figure delimited by a certain number of segments, which are called sides . When the polygon has three sides , it's called triangle .
According to its characteristics, it is possible to distinguish between several kinds of triangles. The aquiangular triangles are those whose three internal angles are acute as 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 I had an angle that measures 90º instead it would be a right triangle by the presence of the right angle. On the other hand, if one of its angles were obtuse (more than 90º ), would receive the qualification of obtuse triangle .
It is important to note that the acute triangles and the obtuse triangles are also part of the group of oblique triangles , denomination that alludes to that none of the internal angles is right.
If we focus on the measures of their sides, the right angles can also be included in other sets. There are acute triangles that are also equilateral triangles because its three sides measure the same. Other acute triangles are isosceles triangles , with two identical sides and a different one. Acute triangles, finally, can be scalene triangles If all three sides have different lengths.
Taking into account the above, 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 allude to different features of the figures.
In addition to all of the above, we cannot ignore that this type of triangle that concerns us comes to fulfill the set of singularities and characteristics attributed to triangles in general:
-The sum of two of its sides is greater than the length of the third side.
-In the acute triangle it is clear, because it is fulfilled, what is known as the sine theorem.
- If two midpoints of two of the sides of the mentioned 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 the other.
-The sum of what are the internal angles that it has come to add 180º.