What were the reasons that the US joined the Korean War?

The United States entered the Korean war because after world war 2, The Soviet Union decided to try to make Korea a communist state. Korea at that time was finally free from rule of the Japanese. The United States saw that The Soviet Communist influence could become a problem if it were to expand it's empire into Korea. This is where the United States decided to step in to stop the Soviet spread of Communism into Korea. Thus beginning the United States entry into the Korean War.

Korean War was a war between North and South Korea that started from 25th June in 1950 and continued till 27th July, 1953. US supported South Korea in the war and hence actively participated in the Korean War. With North Korea invading South Korea, the war started with major clashes along the border. One of the main reasons of US participating in the war with South Korea was the possibility of Soviet Union to attack Europe in case of victory.
By 1948, half of the South Korea was occupied by US and half of North Korea by Soviet Union. Initially, North Korea easily defeated South Korea and invaded certain areas including Seoul. President Truman was afraid that Soviet Union might capture Europe which took US a lot of time to free the Western Europe from the rule of Nazi.
One of the major reasons was the need to keep the idea of capitalism intact as propagated by US. Without their intervention, South Korea would have gradually become communal and impact the surrounding countries.

The Korean war spanned from June 25, 1950 to July 27, 1953. In 1945, by the end of World War II, Korea was freed from Japanese control. Syngman Rhee ruled the capitalist South Korea while Kim Il-Sung ruled the communist North Korea. By 1948, the country was divided in half along the 38th parallel, with American troops occupying the south and Soviet troops occupying the north half. By the time Soviet and American troops withdrew from Korea, tensions were high enough that the border would not hold.
On June 25th, 1950, North Korea invaded South Korea, advancing across the 38th parallel. The North Korean People's Army easily defeated the Republic of Korea's army, captured the capitol, Seoul, and proceeded to occupy all of South Korea except for Pusan.
The United States joined the Korean War because President Truman wanted to contain the spread of communism. The United States was worried about the Domino Effect. The theory was that if Korea fell to the ideology of communism, so would all surrounding countries. On principle, the Korean War was seen as a threat to America and American values.
When South Korea appealed for support, the United States pushed a resolution through the United States Security Council.