Equilateral triangle

Next, we will see some examples of equilateral triangles:

Equilateral triangle

Examples of equilateral triangles

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.

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:

• Acute triangle
• Obtuse triangle
• Scalene Triangle
• Isosceles Triangle
• The edges of a triangle
• Area of a right triangle
• Height of a triangle
• How to calculate the area of a triangle
• How to calculate the perimeter of a triangle?

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

Given the triangle $\triangle ACB$ equilateral

Task:

What is the value of angle $∢ACB$?

Solution:

Given the equilateral triangle $∆ ACB$

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

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

Answer:

$60°$

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.

$3\cdot 5=15$

Answer: $3\cdot 5=15$

Given the equilateral triangle:

Task:

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 $X$.

$33:3=11$

Answer: $11$

In the figure we are given an equilateral triangle.

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

For each side there is a semicircle.

Task:

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

Solution:

$S=S1+3S_2$

When $S=$ the area of the whole figure

Area of the triangle $S_1=$

Area of the semicircle $S_2=$

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

$3.5=\frac{1}{2}\cdot7=DC=BD$

Right triangle: $∆\text{ADC}$

We perform pythagoras:

$AD²+DC²=AC²$

$AD²+3.5²=7²$

$AD²+DC²=AC²$

$AD²=\frac{7\sqrt{3}}{2}$

$S_1=\frac{AD\cdot BC}{2}=\frac{\frac{7\sqrt{3}}{2}\cdot7}{2}≈21.22\operatorname{cm}²$

$S_{2=}\frac{1}{2}(Diámetro del círculo=7 cm)=\frac{1}{2}(radio 3.5\operatorname{cm})$

$S_{2=}=\frac{1}{2}\cdot π\cdot 3.5²=\frac{1}{2}\cdot 3.14\cdot 3.5²$

$≈19.23$

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

Answer: $78.91$

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?

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.