1. **State the problem:** We are given a triangle with side lengths 10, 10, and 13, and we need to determine what kind of triangle it is. 2. **Recall triangle classification rules:** - An **equilateral triangle** has all three sides equal. - An **isosceles triangle** has exactly two sides equal. - A **scalene triangle** has all sides of different lengths. 3. **Analyze the given sides:** - Side 1 = 10 - Side 2 = 10 - Side 3 = 13 4. **Compare the sides:** - Side 1 equals Side 2 (both 10), but Side 3 is different (13). 5. **Conclusion:** Since exactly two sides are equal and the third is different, the triangle is **isosceles but not equilateral**.