Final answer:
Athletics became part of schools in the United States in the late 19th century, as indicated by the advent of college football and the invention of basketball during that period.
Step-by-step explanation:
Athletics became part of schools in the United States in the late 19th century. The evidence for this can be seen in the emergence of college football rivalries that were already legendary by 1902 and the first college football matches dating back to the 1870s.
This period saw the institutionalization of competitive sports in college settings, with increasing numbers of intercollegiate competitions and growing audiences. It was also during this time that James Naismith invented basketball in 1891, further contributing to the sporting activities available in educational institutions.