What do you call a triangle that has three congruent sides and angles?

A triangle with three congruent sides and angles is specifically referred to as an equilateral triangle. In an equilateral triangle, not only are all three sides equal in length, but all three interior angles are also equal, each measuring 60 degrees. This property makes the triangle highly symmetrical and is a key defining characteristic of equilateral triangles.

The isosceles triangle, for example, is defined by having at least two sides of equal length and thus at least two angles that are equal, but it does not require all three sides to be the same. A scalene triangle has all sides of different lengths and, consequently, all angles of different measures. An obtuse triangle is defined by having one angle that is greater than 90 degrees, which does not pertain to the side lengths at all. Therefore, the best description for a triangle with three congruent sides and angles is the equilateral triangle.