Final answer:
Roosevelt referenced Cuba in the context of the Rough Riders and the Spanish-American War, Panama in relation to the construction of the Panama Canal and upholding the Monroe Doctrine, and the Open Door policy in China aimed at ensuring equal trade rights for all nations.
Step-by-step explanation:
The historical events that Roosevelt referenced pertaining to Cuba, Panama, and the Open Door in China have had a significant impact on U.S. foreign policy and international relations during the early 20th century.
A) Cuba
In reference to Cuba, Roosevelt's military involvement during the Spanish-American War is notable, especially with his cavalry unit known as the Rough Riders. The U.S. intervention in Cuba aimed to assist in the Cuban struggle for independence and ultimately led to Cuba's liberation from Spanish rule following the war.
B) Panama
Regarding Panama, Roosevelt facilitated and supported the Panamanian Revolution in order to secure the rights to build the Panama Canal. The Roosevelt Corollary to the Monroe Doctrine further asserted the U.S. role as an international police power in Latin America, intervening to ensure stability and prevent European influence.
C) The Open Door in China
For the Open Door policy in China, Secretary of State John Hay proposed that all nations should have equal trading rights in China. Roosevelt backed this policy, which was aimed at preventing any one nation from monopolizing Chinese trade and allowed American goods to compete freely in Chinese markets.