Math

An overview of equilateral triangle

In the domain of geometry an equilateral triangle is a triangle where all its sides are equal.  Breaking down the term equilateral means equi that means equivalent and conversely lateral are the sides. It is also termed as regular polygon where all the three sides are equal.  Before proceeding ahead there are various aspects of equilateral triangle that you need to be aware.

More about anequilateral triangle?

An equilateral triangle is a triangle where all the three sides are equal. Even the angles turn out to be equal. Since the value of every equilateral triangle is 60 degrees, it is termed as equiangular triangle. Some people may consider it as a regular polygon or a regular triangle as all the sides along with the angles turn out to be equal.

Normally the division of triangles is split into three categories and the classification occurs based on sides. It is an isosceles triangle, equilateral triangle and scalene triangle. Among all of then an equilateral triangle differs from a scalene and an isosceles triangle.

  • If it is an isosceles triangle, then two sides are equal and opposite angles of both the sides are also equal
  • When it is a scalene triangle all sides and angles are not equal
  • Coming to an equilateral triangle all the sides along with the angles turn out to be equal

The properties of an equilateral triangle

There are some properties of an equilateral triangle which classifies a triangle as an equilateral one. Let us get to the properties which make their identification an easy one

  • The sides of an equilateral triangle turn out to be easy in terms of measurements
  • The angles of an equilateral triangle turn out to be concurrent as it would be equal to around 60 degrees
  • A form of a regular polygon since it possess three sides
  • A  perpendicular that is being drawn from an opposite vertex which is to the opposite of an equilateral triangle is known to bisect the angle into equal lengths. It is known to bisect the vertex into equal halves. Ideally it is around 30 degrees from where you are drawing the perpendicular.
  • A point to consider is the sum of all the angles in an equilateral triangle is equal to 180 degrees
  • Coming to the area of equilateral triangle, it is √3a2/ 4 where a appears to be the side of an equilateral triangle.
  • The perimeter of an equilateral triangle is 3 a where a would be the side of an equilateral triangle.
  • The centroid and ortho- centre would be at a particular point.

The perimeter of an equilateral triangle

In geometry the perimeter of any polygon would be equivalent to the sides. When it is an equilateral triangle, the perimeter would be the sum of all sides AB+ BC+ AC of a triangle ABC.

P= a+a+a where a is going to be the length of all the triangles

The centroid of an equilateral triangle

The centroid of an equilateral triangle lies at the sides. As all the sides turn out to be equal it is easy to locate the centroid for the same. To locate the centroid we would need to draw perpendiculars that would be equal in length and at a single point is going to intersect with each other and it is referred to as centroid.

To sum up things, the circumcentre of an equilateral triangle would be at the intersection perpendicular of the bisectors of the sides. Now the circumcircle would be passing through all the three vertices of a triangle. These are the prominent features of an equilateral triangle.

REX

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