Triangles – Properties of Equilateral Triangle


Do you know what a triangle is? A triangle is defined as a closed form that has three angles, three sides, and three vertices. ABC is the abbreviation for a triangle with three vertices that say A, B, and C. The other name for an equilateral triangle is known as a trigon or three-sided polygon. 

If you look at the shape of signboards and your favorite sandwiches, you will see that they create the shape of a triangle. In this article, we’ll go over all there is to know about triangles, types of triangles as well as the properties of equilateral triangles.

Do you want to know more about triangles and equilateral triangles? You can visit the Cuemath website to understand the topic in a fun and easy way!

What is an Equilateral Triangle?

We have already discussed the various types of equilateral triangles in the article above. Let’s know more about equilateral triangles in detail. An equilateral triangle is the one in which all the three sides of the triangle measure the same. Let’s say for example, we have a triangle ABC, then the sides AB = BC = CA. 

In addition, there are three angles in an equilateral triangle like any other triangle, all three of these are congruent and equal to 60 degrees. The total of an equilateral triangle’s three angles is equal to 180 degrees 60° + 60° + 60° which equals 180° As a result, it obeys the angle sum property of triangles.

Properties of Equilateral Triangles

  • Each of the three sides of an equilateral triangle is equal.
  • Each of the three angles of an equilateral triangle is congruent as well as equals 60 degrees.
  • An equilateral triangle has three sides and is a regular polygon.
  • The perpendicular traced from the equilateral triangle’s vertex to the opposite side divides it into equal halves. Furthermore, the angle formed by the vertex from which the perpendicular is drawn is split into two equal angles of 30 degrees each.
  • The ortho-center and centroid of an equilateral triangle are both located at the same location.
  • The median, angle bisector, and height for all sides of an equilateral triangle are all the same.
  • 3*a is the perimeter of an equilateral triangle, where a is the side of the triangle.

Types of Triangles

Do you know that there are different types of triangles, let’s discuss them.

Acute Triangle –The biggest angle in the triangle on the left is 70 degrees, as we can see. Because 70 is less than 90, this is an acute triangle. Always keep in mind that sharp angles are less than 90 degrees. This one is simple to remember because “cute” objects are frequently little, such as puppies and kittens.

Right Angle Triangle – We can observe that the biggest angle in the middle triangle is exactly equal to 90 degrees. Because a 90-degree angle is a right angle, this triangle is known as a right triangle.

Obtuse Triangle – Finally, the biggest angle in the triangle on the right is equal to 117 degrees. This is an obtuse angle since it is more than 90 degrees, hence we name this triangle an obtuse triangle.

Equilateral Triangle – All three sides of the triangle on the left are the same length.   An equilateral triangle is one with all of its sides the same length as this one. It’s not a difficult name to remember because the word equilateral sounds similar to the word equal, as well as the word lateral implies “side.”

Isosceles Triangle – Two of the sides of the center triangle are the same length.  When two sides of a triangle are the same length, the triangle is said to be isosceles. It’s difficult to spell, but it’s easy to identify!

Scalene Triangle – Because none of the sides of our final triangle have the same length, we name it a scalene triangle.