# Private Math Tutor and Equilateral Triangle

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147 A private math tutor can help your child build skills, get ahead in class and reinforce lessons learned in school. When looking into private tutoring, however, you need to consider how it can meet your child’s academic needs and how it will fit into their daily routine. Equilateral triangles have three congruent sides. Equilateral triangles have three angles of 60 degrees each. An equilateral triangle is also referred to as an equiangular triangle since the angles are all equal. Let’s take a look more in detail at an equilateral triangle.

## What is an Equilateral Triangle?

Equilateral triangle have three equal sides and three equal angles, and they are special cases of isosceles triangles. In an equilateral triangle, all three sides are equal in length and all three angles are also equal, making each angle measure 60°.

## Shape of Equilateral Triangle

• An equilateral triangle has three equally long sides.
• The word “equilateral” has its origins in the Latin words aequus, meaning “equal”, and later, meaning “sides”.
• It can refer to any shape that resembles the classical equilateral triangle but usually refers to the regular equilateral triangle: an equilateral triangle that is also equiangular (an equiangular triangle).
• In Euclidean geometry, an equilateral triangle is also equiangular; that is, all three internal angles are also congruent to each other and are each 60°.
• It is also a regular polygon which means that all three sides are the same length.
• The above definition applies only to true triangles. If any of the angle measures are greater than or equal to 180° (straight angle), then the sides must be extended for it to resemble a true triangle.

## Properties of Equilateral Triangle

1. Triangular shapes have equal-length sides.
2. The altitude drawn from any vertex is of equal length.
3. Median drawn from any vertex divides the opposite side into two parts, each of which is half the length of the base (or altitude).
4. In an equilateral triangle, the circumcenter coincides with the incenter and centroid and so they all lie on a single line (Euler’s line).
5. The orthocenter, centroid, incenter, and circumcenter all coincide with one another at a single point which is called the center of gravity or center.
6. In an equilateral triangle, ABC let G be the centroid, H is the orthocenter, I be the incenter and O be the circumcenter then AH coincides with IG which passes through O.

## What is Equilateral Triangle Theorem?

• One thing to remember about an equilateral triangle is that the three sides are congruent, which means that all three sides are equal in length.
• Another thing to remember about an equilateral triangle is that the three angles are congruent, which means that all three angles measure 60 degrees each.
• Yet another thing to remember about an equilateral triangle is that all three sides are parallel as well as perpendicular to each other.

## Area of Equilateral Triangle

An equilateral triangle is a special kind of triangle with equal sides. The best way to remember this shape is to think that all the sides are the same length (equal). To find the area of an equilateral triangle, you will need to use this formula:
area = [base * height] / 2

You will notice that in this formula we have to use the base and height. You should understand how to calculate these by now, so don’t worry too much about it.
It’s important that you remember what these represent, however, as they mean different things depending on which type of triangle you’re dealing with.
The base refers to any one of the three sides and the height is a line drawn through one vertex at a right angle (perpendicular) to another side. Want to learn more about the equilateral triangles, visit the Cuemath website to learn more about math.