What type of triangle is shown if all sides are equal in length?

When all sides of a triangle are equal in length, the triangle is classified as an equilateral triangle. This specific property of equilateral triangles means that not only are all three sides the same, but all three internal angles are also equal, each measuring 60 degrees. This symmetry and equality across all sides and angles is what fundamentally defines an equilateral triangle.

In contrast, an isosceles triangle has at least two sides that are equal in length, and while this is similar, equilateral triangles take it a step further by having all three sides equal. A right triangle is characterized by having one angle that measures exactly 90 degrees, which does not necessarily correlate to any specific relation between side lengths. Lastly, an obtuse triangle contains one angle that is greater than 90 degrees, which also does not relate to having equal side lengths. Thus, the defining feature of having equal sides confirms that the correct classification of the triangle in question is equilateral.