Final answer:
The property associated with the transitive property of parallel lines is similarity, which describes the relation where if line A is parallel to line B and B to C, then A is parallel to C.
Step-by-step explanation:
The property associated with the transitive property of parallel lines is similarity. The transitive property essentially states that if one element (in geometry, this could be a line or angle) is related to a second element, and the second element is related to a third element in the same way, then the first element is also related to the third element. In the context of parallel lines, if line A is parallel to line B, and line B is parallel to line C, then line A is also parallel to line C, demonstrating similarity.