Which type of triangle has all sides equal?

The correct answer is the equilateral triangle, which is defined by the property that all three of its sides are of equal length. This equality of sides also leads to all three interior angles being equal, each measuring 60 degrees. This characteristic makes equilateral triangles uniquely symmetric and balanced, contributing to their prominence in various mathematical applications and geometric discussions.

In contrast, an isosceles triangle has only two sides of equal length, which distinguishes it from the equilateral triangle. A scalene triangle features three sides of different lengths, making it the least symmetric of the triangle types. Finally, a right triangle is specifically defined by having one angle that is exactly 90 degrees, and it can have varying side lengths that do not necessarily relate to one another equally. Thus, equilateral triangles are the only type among the choices provided that has all sides equal.