What type of triangle has three sides of equal length and three angles of equal measure, each measuring 60 degrees?

An equilateral triangle is defined by having three sides of equal length and three angles of equal measure, each measuring 60 degrees. This specific property of equal lengths and equal angles is what distinguishes an equilateral triangle from other types of triangles.

In an equilateral triangle, since all sides are the same length, the corresponding angles must also be the same due to the properties of triangles, which state that the sum of the interior angles always equals 180 degrees. Therefore, dividing 180 degrees equally among three angles results in each angle measuring 60 degrees.

This characteristic makes the equilateral triangle unique compared to other triangle types. For instance, a scalene triangle has no sides of equal length and no angles that are the same. An isosceles triangle, while it has at least two sides of equal length, does not require all three sides to be equal or all angles to measure the same. An acute triangle is defined by having all angles measuring less than 90 degrees, which can include equilateral triangles, but does not specifically refer to the equal side lengths.

Thus, the properties of an equilateral triangle distinctly characterize it, making it the correct answer.