What is Black Tuesday and why does it mark the beginning of the Great Depression?

you basically answered your own question but OK.

Explanation:

October 29, 1929. On this date, share prices on the New York Stock Exchange completely collapsed, becoming a pivotal factor in the emergence of the Great Depression.

The DJIA fell 12%, one of the largest one-day drops in stock market history. More than 16 million shares were traded in the panic sell-off, which effectively ended the Roaring '20s and led the global economy into the Great Depression.

the   square   deal   was   a   program   where   the   government gave any one   a fair   chance   to succeed

i believe the answer is a