1. The problem asks about the properties of an equilateral triangle, specifically the relationship between its sides. 2. An equilateral triangle is defined as a triangle where all three sides are equal in length. 3. Therefore, the sides satisfy the condition $a = b = c$. 4. This means that the correct choice is the one where all sides are equal. 5. Hence, the answer is option c) $a = b = c$. This is because by definition, an equilateral triangle has all sides equal, and this equality also implies all angles are equal (each $60^\circ$).