An equilateral triangle is a type of triangle in which all three sides are of equal length, and consequently, all three interior angles are equal. In other words, an equilateral triangle is characterized by its symmetry and uniformity in side lengths and angles.

Key features of an equilateral triangle:-

  1. Side Lengths: All three sides of the triangle are of equal length. Mathematically, if a, b, and c are the side lengths of the triangle, then a = b = c.
  2. Angles: All three interior angles have equal measures. Mathematically, if A, B, and C are the angles opposite sides a, b, and c respectively, then A = B = C.

Here's an illustration of an equilateral triangle:


In the above triangle ABC:

  • All three side lengths a, b, and c are equal.
  • All three angles A, B, and C have equal measures.

Equilateral triangles have several interesting properties:-

  • The interior angles of an equilateral triangle each measure 60 degrees.
  • The circumcenter (the point equidistant from all three vertices) and the incenter (the point equidistant from all three sides) coincide at the centroid of the triangle.
  • The equilateral triangle is the only regular polygon with three sides.

Equilateral triangles are commonly encountered in geometry and are fundamental shapes in various mathematical and scientific contexts.