An equilateral triangle has three equal sides.
Triangles are polygons : flat figures that are made up of a series of segments. In the specific case of triangles, they are polygons composed of three segments (or three sides ).
When the three sides of the triangle are equal , we have an equilateral triangle . This means that the three sides of the equilateral triangle have the same length; therefore, they measure the same.
The etymology
It is important that we know the etymological origin of the term equilateral triangle . In this case we can say that the two words that make it up come from Latin:
-Triangle is the result of the sum of two components: the prefix "tri- ", which means "three", and the noun angulus , which is equivalent to "corner".
– Equilateral derives from what aequilaterus is. This word is made up of two words: aequus , which is synonymous with "equal", and laterus , which means "side".
Characteristics of an equilateral triangle
Equilateral triangles, in turn, are equiangular since their three internal angles also measure the same ( 60º ). Since these three angles are acute because they measure less than 90º, they are acute triangles .
It is important to keep in mind that the same triangle, in this way, can be equilateral , equiangular and acute angled . The three qualifications refer to different characteristics of the same figure. There are, however, no equilateral triangles that are right or obtuse , since there is no possibility of these triangles having a right angle or an obtuse angle.
It is possible to find equilateral triangles in different places and contexts.
Formulas and calculations
Since the three sides of an equilateral triangle are equal, the perimeter of this type of triangle can be calculated by multiplying the length of any of the sides by three. If one of the sides of an equilateral triangle measures 24 centimeters , we know that the other two will also measure the same. To calculate the perimeter, simply multiply one side by three: 24 centimeters x 3 = 72 centimeters . This result, on the other hand, can be reached simply by adding the length of the three sides: 24 centimeters + 24 centimeters + 24 centimeters = 72 centimeters .
Other formulas that exist to calculate the characteristics of the equilateral triangle are the following:
-In order to find the value of its height, we must proceed to use the famous Pythagorean Theorem. Specifically, this will mean taking the square root of 3a (a is the hypotenuse) and dividing the result by two.
-In the event that you want to discover the value of its area, what you have to undertake is to calculate one half of the base times the height.
Equilateral, isosceles and scalene triangles
Whenever we talk about equilateral triangles, two other types come to mind that are opposite to the previous ones but have in common that they are fundamental within the classifications of this type of geometric figures. We are referring to these:
– Isosceles triangle . It is one that is identified because it has two equal sides and also two equal angles.
– Scalene triangle . It is the one that is characterized because it has three sides that are different from each other and their angles are not equal either.