1. The problem asks us to classify a triangle with all three sides measuring 9 inches each. 2. The key formula or rule here is that a triangle with all three sides equal is called an equilateral triangle. 3. Since all sides are equal ($9 = 9 = 9$), the triangle is equilateral. 4. An equilateral triangle also has all angles equal to 60 degrees, but the problem only asks for classification by side lengths. 5. Therefore, the triangle is an equilateral triangle. **Final answer:** The triangle is an equilateral triangle.