Remember: If two lines areparallel to a line, then the two lines are parallel to each other.
So, if A and C are parallel and also B and C are parallel, then A and B are parallel.
Hence, statement 1 is correct
Remember: If two lines are perpendicular to a line, then the two lines are parallel to each other.
So, if A is perpendicular to C and B is perpendicular to C, then A and B are parallel.
Hence, statement 2 is correct
If the acute angle between A and C is equal to the acute angle between B and C, then A and B are parallel as the alternate angles formed are equal.
Hence, statement 3 is correct.