The equilateral triangle is a triangle that all its sides have the same length.

This also implies that all its angles are equal, that is, each angle measures $60°$ degrees (remember that the sum of the angles of a triangle is $180°$ degrees and, therefore, these $180°$ degrees are divided equally by the three angles).

Recall that within a triangle there are what are called remarkable lines, which are the heights, medians, perpendicular bisectors and bisectors, these lines intersect at the so-called remarkable points (orthocenter, barycenter, circumcenter and incenter respectively).

In an equilateral triangle, the remarkable lines coincide.

In an equilateral triangle, the remarkable points coincide at the same point.

Recall that triangles can be classified according to the measure of their interior angles. Within this classification we find the acute triangles which are characterized by having all its acute angles (less than $90°$ degrees).

Since an equilateral triangle has all its interior angles equal to $60°$ degrees, it is also an acute triangle.

If you are interested in learning more about other triangle topics, you can enter one of the following articles:

The perimeter of the triangle is equal to $33 cm$. What is the value of $X$?

Solution:

Since we are given an equilateral triangle whose perimeter is $33 cm$, all we have to do is divide the circumference by 3 and we get the side measure $X$.

Ejemplos y ejercicios con soluciones de triángulo equilátero

Exercise #1

Calculate the size of angle X given that the triangle is equilateral.

Video Solution

Step-by-Step Solution

Remember that the sum of angles in a triangle is equal to 180.

In an equilateral triangle, all sides and all angles are equal to each other.

Therefore, we will calculate as follows:

$x+x+x=180$

$3x=180$

We divide both sides by 3:

$x=60$

Answer

60

Exercise #2

Choose the appropriate triangle according to the following:

Angle B equals 90 degrees.

Video Solution

Step-by-Step Solution

Let's note in which of the triangles angle B forms a right angle, meaning an angle of 90 degrees.

In answers C+D, we can see that angle B is smaller than 90 degrees.

In answer A, it is equal to 90 degrees.

Answer

Exercise #3

Given the values of the sides of a triangle, is it a triangle with different sides?

Video Solution

Step-by-Step Solution

As is known, a scalene triangle is a triangle in which each side has a different length.

According to the given information, this is indeed a triangle where each side has a different length.

Answer

Yes

Exercise #4

In a right triangle, the sum of the two non-right angles is...?

Video Solution

Step-by-Step Solution

In a right-angled triangle, there is one angle that equals 90 degrees, and the other two angles sum up to 180 degrees (sum of angles in a triangle)

Therefore, the sum of the two non-right angles is 90 degrees

$90+90=180$

Answer

90 degrees

Exercise #5

Is the triangle in the drawing a right triangle?

Step-by-Step Solution

Due to the presence of the 90 degree angle symbol we can determine that this is indeed a right-angled triangle.

Answer

Yes

Questions on the subject

What is an equilateral triangle for children?

It is a geometric figure formed by three equal sides.

Why is the triangle equilateral?

Because its three sides have the same length.

What are the angles of an equilateral triangle?

In an equilateral triangle its interior angles are acute and these measure $60°$ degrees each.

What is an equilateral, isosceles and scalene triangle?

They are geometric figures with three sides, the first one is characterized by having all its sides equal, the second one by having two equal sides and the third one by not having any equal side.

What is another name for the equilateral triangle?