Equilateral triangle

🏆Practice types of triangles

Definition of equilateral triangle

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° 60° degrees (remember that the sum of the angles of a triangle is 180° 180° degrees and, therefore, these 180° 180° degrees are divided equally by the three angles).

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In a right triangle, the side opposite the right angle is called....?

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Next, we will see some examples of equilateral triangles:

Equilateral triangle

A2 - image of equilateral triangle

Examples of equilateral triangles

A3-Examples of equilateral triangles


Another name for the equilateral triangle

Recall that a regular polygon is a geometric figure that:

  • Has all its sides equal
  • Has all its angles equal

Therefore, the equilateral triangle is also known as the regular three-sided polygon.

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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° 90° degrees).

Since an equilateral triangle has all its interior angles equal to 60° 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:

On the Tutorela blog you will find a variety of articles about mathematics.


Equilateral Triangle Exercise

Exercise 1

image Given equilateral triangle ABC

Given the triangle △ACB \triangle ACB equilateral

Task:

What is the value of angle ∢ACB ∢ACB ?

Solution:

Given the equilateral triangle ∆ACB ∆ ACB

In an equilateral triangle all its angles are 60° 60° .

Therefore the angle ∢ACB ∢ACB is equal to 60° 60°

Answer:

60° 60°


Do you know what the answer is?

Exercise 2

Given the equilateral triangle:

Exercise 2 Given the equilateral triangle

Homework:

What is the perimeter?

Solution:

Since we are given an equilateral triangle, we will multiply the given side by 3 and get the perimeter of the triangle.

3⋅5=15 3\cdot 5=15

Answer: 3⋅5=15 3\cdot 5=15


Exercise 3

Given the equilateral triangle:

Exercise 3 Given the equilateral triangle

Task:

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

Solution:

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

33:3=11 33:3=11

Answer: 1111


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Exercise 4

In the figure we are given an equilateral triangle.

The length of each side is equal to 7cm 7 cm

For each side there is a semicircle.

Exercise 4 In the figure we are given an equilateral triangle

Task:

What is the area of the whole figure? Replace a π=3.14 \pi=3.14

Solution:

S=S1+3S2 S=S1+3S_2

When S= S= the area of the whole figure

Area of the triangle S1= S_1=

Area of the semicircle S2= S_2=

In an equilateral triangle the height merges with the middle and so when AD⊥BCAD⊥BC

3.5=12⋅7=DC=BD 3.5=\frac{1}{2}\cdot7=DC=BD

Right triangle: ∆ADC ∆\text{ADC}

We perform pythagoras:

AD2+DC2=AC2 AD²+DC²=AC²

AD2+3.52=72 AD²+3.5²=7²

AD2+DC2=AC2 AD²+DC²=AC²

AD2=732 AD²=\frac{7\sqrt{3}}{2}

S1=AD⋅BC2=732⋅72≈21.22cm⁡2 S_1=\frac{AD\cdot BC}{2}=\frac{\frac{7\sqrt{3}}{2}\cdot7}{2}≈21.22\operatorname{cm}²

S2=12(Diaˊmetrodelcıˊrculo=7cm)=12(radio3.5cm⁡) S_{2=}\frac{1}{2}(Diámetro del círculo=7 cm)=\frac{1}{2}(radio 3.5\operatorname{cm})

S2==12⋅π⋅3.52=12⋅3.14⋅3.52S_{2=}=\frac{1}{2}\cdot π\cdot 3.5²=\frac{1}{2}\cdot 3.14\cdot 3.5²

≈19.23 ≈19.23

S=21.22+3⋅19.23=78.91 S=21.22+3\cdot 19.23=78.91

Answer: 78.91 78.91


Ejemplos y ejercicios con soluciones de triángulo equilátero

Exercise #1

What kind of triangle is given in the drawing?

404040707070707070AAABBBCCC

Video Solution

Step-by-Step Solution

As all the angles of a triangle are less than 90° and the sum of the angles of a triangle equals 180°:

70+70+40=180 70+70+40=180

The triangle is isosceles.

Answer

Isosceles triangle

Exercise #2

Which kind of triangle is given in the drawing?

666666666AAABBBCCC

Video Solution

Step-by-Step Solution

As we know that sides AB, BC, and CA are all equal to 6,

All are equal to each other and, therefore, the triangle is equilateral.

Answer

Equilateral triangle

Exercise #3

What kid of triangle is the following

393939107107107343434AAABBBCCC

Video Solution

Step-by-Step Solution

Given that in an obtuse triangle it is enough for one of the angles to be greater than 90°, and in the given triangle we have an angle C greater than 90°,

C=107 C=107

Furthermore, the sum of the angles of the given triangle is 180 degrees so it is indeed a triangle:

107+34+39=180 107+34+39=180

The triangle is obtuse.

Answer

Obtuse Triangle

Exercise #4

What kind of triangle is given in the drawing?

999555999AAABBBCCC

Video Solution

Step-by-Step Solution

Given that sides AB and AC are both equal to 9, which means that the legs of the triangle are equal and the base BC is equal to 5,

Therefore, the triangle is isosceles.

Answer

Isosceles triangle

Exercise #5

What kind of triangle is given here?

111111555AAABBBCCC5.5

Video Solution

Step-by-Step Solution

Since none of the sides have the same length, it is a scalene triangle.

Answer

Scalene triangle

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° 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?

A regular three-sided polygon.


What are the types of triangles?

If the classification is made with respect to their sides we have three types of triangles: equilateral, isosceles and scalene.

If the classification is made with respect to their angles we also find three types of triangles: acute-angled, right-angled and obtuse-angled.


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