for a triangle? A. $8,8,9$ B. $4,9,4$ C. $3,8,12$

Step 1 ：Given sets of numbers are A. $8,8,9$, B. $4,9,4$, and C. $3,8,12$. We need to check if these sets can form a triangle.

Step 2 ：A triangle can be formed if the sum of the lengths of any two sides is greater than the length of the third side. This is known as the triangle inequality theorem.

Step 3 ：Let's check each option one by one.

Step 4 ：For option A, the sum of any two sides is greater than the third side, so it can form a triangle.

Step 5 ：For option B, the sum of the two sides (4, 4) is equal to the third side (9), which does not satisfy the triangle inequality theorem, so it cannot form a triangle.

Step 6 ：For option C, the sum of the two smaller sides (3, 8) is less than the third side (12), which does not satisfy the triangle inequality theorem, so it cannot form a triangle.

Step 7 ：The sets of numbers that can form a triangle are: A. $8,8,9$ \(\boxed{True}\), B. $4,9,4$ \(\boxed{False}\), C. $3,8,12$ \(\boxed{False}\)