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).
Therefore, the equilateral triangle is also known as the regular three-sided polygon.
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Test your knowledge
Question 1
Can a right triangle be equilateral?
Incorrect
Correct Answer:
No
Question 2
Choose the appropriate triangle according to the following:
Angle B equals 90 degrees.
Incorrect
Correct Answer:
Question 3
Does every right triangle have an angle _____ The other two angles are _______
Incorrect
Correct Answer:
Straight, sharp
Other characteristics of equilateral triangles
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:
Ejemplos y ejercicios con soluciones de triángulo equilátero
Exercise #1
Is the triangle in the drawing an acute-angled triangle?
Video Solution
Step-by-Step Solution
An acute-angled triangle is defined as a triangle where all three interior angles are less than 90∘.
In examining the visual depiction of the triangle provided in the problem, we need to see if it appears to satisfy this property. The assessment relies on observing the triangle's structure shown in the drawing and noting any geometric indications suggesting angle types.
Given the information from the drawing, if all angles seem to satisfy the condition of being less than 90∘, then by definition, the triangle is an acute-angled triangle.
Conclusively, the answer to whether the triangle is acute-angled based on provided visual assessment and inherent assumptions in its illustration is: Yes.
Answer
Yes
Exercise #2
In an isosceles triangle, the angle between ? and ? is the "base angle".
Step-by-Step Solution
An isosceles triangle is one that has at least two sides of equal length. The angles opposite these two sides are known as the "base angles."
The side that is not equal to the other two is referred to as the "base" of the triangle. Thus, the "base angles" are the angles between each of the sides that are equal in length and the base.
Therefore, when we specify the angle in terms of its location or position, it is the angle between a "side" and the "base." This leads to the conclusion that the angle between the side and the base is the "base angle."
Therefore, the correct choice is Side, base.
Answer
Side, base.
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
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
Exercise #5
In an isosceles triangle, what are each of the two equal sides called ?
Step-by-Step Solution
In an isosceles triangle, there are three sides: two sides of equal length and one distinct side. Our task is to identify what the equal sides are called.
To address this, let's review the basic properties of an isosceles triangle:
An isosceles triangle is defined as a triangle with at least two sides of equal length.
The side that is different in length from the other two is usually called the "base" of the triangle.
The two equal sides of an isosceles triangle are referred to as the "legs."
Therefore, each of the two equal sides in an isosceles triangle is called a "leg."
In our problem, we confirm that the correct terminology for these two equal sides is indeed "legs," distinguishing them from the "base," which is the unequal side. This aligns with both the typical definitions and properties of an isosceles triangle.
Thus, the equal sides in an isosceles triangle are known as legs.
Answer
Legs
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?