Can segments 9, 9, and 1 form a triangle

Yes, segments 9, 9, and 1 can form a triangle. The rule that determines this is called the Triangle Inequality Theorem. This states that for a triangle with side lengths A B and C to exist, the following relationships have to apply:
A + B > C
B + C > A
A + C > B
With side lengths 9, 9, 1, this rule applies.
9 + 9 > 1
9 + 1 > 9
1 + 9 > 9
Therefore, a triangle will be able to be formed from the side lengths.