Which triangle necessarily has all sides equal and all angles equal?

A triangle that has all sides equal and all angles equal is defined as equilateral. In an equilateral triangle, not only are the lengths of the sides the same, but each of the interior angles measures exactly 60 degrees. This property ensures that all angles and sides are congruent, which is a defining characteristic of an equilateral triangle.

Understanding the other types of triangles helps clarify why they do not meet these criteria. An isosceles triangle has at least two sides that are equal but does not require all three sides to be equal, nor does it guarantee that all angles will be the same. A scalene triangle is characterized by all sides and all angles being different, making it impossible for a scalene triangle to have equal sides or angles. An obtuse triangle contains one angle that is greater than 90 degrees, and it does not necessarily have equal sides or angles.

Therefore, the unique properties of an equilateral triangle make it the correct answer, as it is the only type of triangle where all sides and all angles are necessarily equal.