1. The problem asks if a triangle can have side lengths 1, 2, and 3. 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 be true: $$a + b > c$$ $$a + c > b$$ $$b + c > a$$ 3. Let's check these inequalities with sides 1, 2, and 3: - $1 + 2 = 3$ which is not greater than 3 (it is equal). - $1 + 3 = 4$ which is greater than 2. - $2 + 3 = 5$ which is greater than 1. 4. Since the first inequality $1 + 2 > 3$ is not satisfied (it equals 3, not greater), these side lengths cannot form a triangle. 5. Therefore, the answer is **no**, a triangle cannot have side lengths 1, 2, and 3.