Who is asking: Student
I first want to compliment whoever made the definition that you gave me, "An isosceles triangle is a triangle with at LEAST two congruent sides". The dictionaries that I looked in defined isosceles as "having two equal sides", leaving it to the reader to interpret whether or not this means exactly two. With your definition it is explicit that any triangle with at least two congruent sides is isosceles. Thus a triangle with all sides congruent is both isosceles and equilateral.
The standard way these things are handled in math is to treat
definitions in an inclusive sense. Yes an equilateral
triangle is an isosceles triangle - for each of the three
possible pairs of sides. That means you can apply the
Isosceles Triangle Theorem and conclude that the three angles
of an equilateral triangle are also equal!
Euclid Book I, Definition 20 makes it clear that isosceles triangles have exactly two congruent sides (the "legs") and one side of a different length (called the "base"). He distinguishes the three types of triangles: equilateral (3 congruent sides), isosceles (2 congruent sides but not the third), and scalene (no two congruent). On the other hand, since not everybody knows this rule it is wise to remind the reader when the distinction is important by saying things like "an isosceles triangle that is not equilateral", or "a triangle with exactly two congruent sides."