Concept:
The glass transition temperature ($T_g$) is a critical point for amorphous and semi-crystalline polymers, marking the transition from a hard, brittle state to a soft, rubbery state.
Step 1: Evaluate Assertion A.
Below $T_g$, polymers are in a "glassy" state—hard, rigid, and brittle. Above $T_g$, they enter a "rubbery" or elastomeric state where they are flexible and can be easily deformed. Thus, A is correct.
Step 2: Evaluate Reason R.
The transition at $T_g$ is related to the onset of long-range segmental motion of the polymer chains. Below $T_g$, the thermal energy is too low for chains to slide, making them rigid. Above $T_g$, enough energy exists for segments of 10-50 atoms to move, creating flexibility. Thus, R is correct.
Step 3: Conclusion.
Reason R provides the exact molecular-level explanation for the macroscopic behavior described in Assertion A. Therefore, R is the correct explanation for A.