How are 13th, 14th, and 15th amendments related in terms of their purpose and goals?
The 13th, 14th, and 15th Amendments were ratified in 1865, 1868 and 1870 (respectively) just following the end of the Civil War. They are known as the Civil War Amendments.
The 13th Amendment abolished slavery in all states and all US governed territories.
The 14th Amendment, among other things, provided citizenship to all former slaves and made it illegal for any states to make laws that would infringe upon those rights.
The 15th Amendment gave all citizens the right to vote, regardless of race, color or previous servitude (slavery).
The Emancipation Proclamation officially ended slavery but there was concern that the next official election would see its return. These amendments were all added to make sure slavery would not return if a different party was elected to office or if certain states decided to reinstate it.