Final answer:
The British violated American rights by taxing the colonists without representation and interfering with their trade and self-government.
Step-by-step explanation:
According to the Declaration of Independence, the British had violated American rights in two major ways. First, they had taxed the colonists without representation, meaning that the colonists had no say in the taxes imposed on them. Second, the British had interfered with the colonists' trade and denied them their right to self-government.