1. The problem asks if a triangle can have sides of lengths 1, 9, and 9. 2. To determine this, we use the triangle inequality theorem, which states that for any triangle with sides $a$, $b$, and $c$, the following must hold true: $$a + b > c$$ $$a + c > b$$ $$b + c > a$$ 3. Let's check each inequality with $a=1$, $b=9$, and $c=9$: - $1 + 9 = 10 > 9$ (True) - $1 + 9 = 10 > 9$ (True) - $9 + 9 = 18 > 1$ (True) 4. Since all three inequalities are true, the sides 1, 9, and 9 can form a triangle. **Final answer:** Yes, the sides 1, 9, and 9 can form a triangle.