In the domain of geometry an equilateral triangle is a form of triangle where all the four sides turn out to be equal. Even the three angles that are opposite to each other would be equal in measure. Since each of the angles in an equilateral triangle is 60 degrees it is known as equiangular triangle. Pretty much like the other triangles an equilateral triangle has specific formulas to derive its area, perimeter and formula of height.
The details of equilateral triangle
Just as the name suggests an equilateral triangle is one where all the three sides turn out to be equal. Even the three angles are concurrent to each other and are 60 degrees. The sum of all the three angles of an equilateral triangle is 180 degrees split into 60 degree of each angle. It is an extension of the angle property of a triangle.
An equilateral triangle and the shape of its sides are equal. Basically it is a combination of a couple of words. Even it is referred to as a regular triangle and a regular polygon as all the sides turn out to be equal. Let us explain it with an example in the form of a triangle ABC where AB= BC= AC would be three sides and all of them are equal. In addition the three angles A, B and C are also equal that is 60 degrees. Considering the other types of sides there are a couple of other type of triangles which is the isosceles triangle and Scalene triangle.
In an isosceles triangle only a couple of sides are equal and the angles that are opposite to the equal sides are also equal. Coming to a scalene triangle all the three sides are unequal and all the angles turn out to be unequal in measure
The properties of an equilateral triangle
- The three sides work out to be equal
- The three angles are concurrent and equate to 60 degrees
- It happens to be a regular polygon with three sides equal
- Any perpendicular that is being drawn from the vertex, to the opposite side would bisect it into a couple of equal halves. Even the angle of the vertex from where you draw the perpendicular would be split into two halves. They would be measuring around 30 degrees each
- The centroid and the Ortho- centre appear to be at the same point
- When it is an equilateral triangle, the altitude, angle bisector and median for all the three sides would turn out to be equal.
- The perimeter of an equilateral triangle is 3 a
By now it is obvious that in an equilateral triangle all the three sides and three angles are equal. Based on these properties one tends to arrive at the formula of area of equilateral triangle. Even it is possible to derive the height and perimeter of an equilateral triangle with the same dimensions In addition when we need to calculate the perimeter of an equilateral triangle is the sum of all sides. It would be dividing the triangle into two equal right angles. If we are dropping an altitude from the base of the triangle once again it would be split into two equal halves.
This pretty much concludes what an equilateral triangle is all about. But since it is an important aspect of the curriculum of students they need to have an in depth grasp on the given topic. The best place to educate you on the topic would be Cuemath. Within a short span of time it has gone on to climb the popularity charts.