The sum of the lengths of any two sides of a triangle is greater than the length of the third side. If you take the three sides of a triangle and add them in pairs, the sum is greater than (not equal to) the third side. If that is not true, then it is not possible to construct a triangle with the given side lengths.

The properties of equilateral triangles: All sides are the same length (congruent) and all interior angles are the same size (congruent). To find the measure of the interior angles, we know that the sum of all the angles is 180 degrees (from above)... And there are three angles...

A triangle with all sides equal is called equilateral, a triangle with two sides equal is called isosceles, and a triangle with all sides a different length is called scalene.

A triangle with all sides equal is called an equilateral triangle, and a triangle with no sides equal is called a scalene triangle. An equilateral triangle is therefore a special case of an isosceles triangle having not just two, but all three sides and angles equal.