What led the us and their allies to get involved in the vietnam war

The  United States and its allies worried that if Vietnam fell to the communists, other countries in Southeast Asia would follow.  This was known as "domino theory" -- that the spread of communism in Vietnam would result in other countries in the region falling like dominoes to the influence of communism.  

President Dwight Eisenhower is the one who initiated the use of the term "domino theory."  In a speech he gave in April, 1954, Eisenhower warned that if French Indochina fell to communism, it very likely could cause a domino  effect in Southeast Asia.  French Indochina is what the region of Vietnam was called during the days of French colonialism there.  The movement against French colonial control was led by Vietnamese nationalist who also happened to be communists.  The Vietamese nationalist / communist movement was led by HoChi Minh.

music

explanation:

roosevelt believed that in light of the country's recent military successes, it was unnecessary to use force to achieve foreign policy goals, so long as the military could threaten force. this belief, and his strategy of “speaking softly and carrying a big stick,” shaped much of roosevelt's foreign policy.