1. The problem asks which set of side lengths will NOT form a triangle. 2. Recall the Triangle Inequality Theorem: For any triangle with sides $a$, $b$, and $c$, the sum of the lengths of any two sides must be greater than the length of the remaining side. 3. Check each set: - A: 10, 20, 30 - $10 + 20 = 30$ which is NOT greater than 30, so this does NOT satisfy the triangle inequality. - B: 6, 8, 10 - $6 + 8 = 14 > 10$, $6 + 10 = 16 > 8$, $8 + 10 = 18 > 6$ all true. - C: 7, 14, 18 - $7 + 14 = 21 > 18$, $7 + 18 = 25 > 14$, $14 + 18 = 32 > 7$ all true. - D: 9, 10, 9 - $9 + 10 = 19 > 9$, $9 + 9 = 18 > 10$, $10 + 9 = 19 > 9$ all true. 4. Only set A fails the triangle inequality. Final answer: The set of side lengths that will NOT form a triangle is A. 10 cm, 20 cm, 30 cm.