Final answer:
Tchaikovsky's ballets remain central to the repertory today.
Step-by-step explanation:
The statement 'Tchaikovsky's ballets remain central to the repertory today' is true. Tchaikovsky is one of the most renowned composers in the history of ballet, and his ballets, such as 'Swan Lake,' 'The Nutcracker,' and 'Sleeping Beauty,' are still performed by many ballet companies around the world. These ballets are considered classics and continue to captivate audiences with their beautiful music, storytelling, and choreography.