Can segments 9, 9, and 1 form a triangle

No they would not 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.