How we cite our quotes: (Sentence)
Quote #1
…whenever any Form of Government becomes destructive of these ends, it is the Right of the People to alter or to abolish it, and to institute new Government, laying its foundation on such principles and organizing its powers in such form, as to them shall seem most likely to effect their Safety and Happiness. (4)
Jefferson writes that first of all, the current government is doing bad things, and second of all, that the colonies have a vision of how to improve the system. His words show that there has been serious thought as to why the colonies must declare independence. To be legitimate, you generally have to have good reasons and know what you're doing, and Jefferson's opening sentences encompass all of that.
Quote #2
Such has been the patient sufferance of these Colonies; and such is now the necessity which constrains them to alter their former Systems of Government. (7)
Not only do the colonies want independence, but they need it. Their hand has effectively been forced by what's been inflicted by the British government.
Quote #3
He has abdicated Government here, by declaring us out of his Protection and waging War against us. (33)
It's kind of hidden in the midst of all the other complaints, but Jefferson flat-out says that the King has given up his control over the colonies through his actions against them, especially after declaring them rebels. Of course the United States are legitimate if the British government has already (albeit unofficially) given up their rule. Do you think this is a convincing argument?
Quote #4
In every stage of these Oppressions We have Petitioned for Redress in the most humble terms: Our repeated Petitions have been answered only by repeated injury. (38)
Jefferson further supports the legitimacy of the colonial declaration by reminding the reader of how much the colonists tried to find another way to resolve their grievances. They tried so hard, but the British wouldn't listen, and actually just amped up the oppression, making everything worse. That makes the desire for full-out independence pretty justifiable.
Quote #5
…as Free and Independent States, they have full Power to levy War, conclude Peace, contract Alliances, establish Commerce, and to do all other Acts and Things which Independent States may of right do. (46)
To close out the Declaration, the final paragraph finally declares independence and establishes a new government of the United States. Here Jefferson and company prove that they know what independence entails, and have thought about the true significance of being their own nation. They're thinking ahead, which further legitimizes the Continental Congress as governmental body. True, there's potentially a lot included under "all other Acts and Things," but if he listed everything it would have been about fifty pages, and no one wants that.