Question

"We hold these truths to be self-evident: that all men are created equal; that they are endowed by their Creator with certain unalienable rights; that among these are life, liberty, and the pursuit of happiness." This quote from the Declaration of Independence best supports the theory of...
  rule of law
   popular sovereignty
   natural rights
   social contract

Answer 1

natural rights

The theory of natural rights was outlined by John Locke during the Enlightenment.

The idea of natural rights essentially supported that by being born and a part of the natural order, people were granted rights by God that no government could take away but rather must support and protect. Thomas Jefferson was a student of the Enlightenment and believed in the ideas of John Locke. This passage of the Declaration of Independence demonstrates Jefferson's view on government and their duty to protect and support those natural rights.

Answer 2

Natural rights

Explanation / historical context:

John Locke was one of the first of the Enlightenment era philosophers. The Enlightenment's emphasis on reason was in contrast to superstition and traditional beliefs.  The Scientific Revolution had shown that there are natural laws in place in the physical world and in the universe at large. Applying similar principles to matters like government and society, Enlightenment thinkers believed that using reason will guide us to the best ways to operate politically so we can create the most beneficial conditions for society.  For John Locke, this included a conviction that all human beings have certain natural rights which are to be protected and preserved.    Locke's ideal was one that promoted individual freedom and equal rights and opportunity for all.  Each individual's well-being (life, health, liberty, possessions) should be served by the way government and society are arranged.

As noted in the section the question quoted, the Declaration of Independence states Locke's natural rights idea in this way:  "We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness."

John Locke, in his Second Treatise on Civil Government (1690), had expressed those same ideas in these words:

• The state of nature has a law of nature to govern it, which obliges every one: and reason, which is that law, teaches all mankind, who will but consult it, that being all equal and independent, no one ought to harm another in his life, health, liberty, or possessions… (and) when his own preservation comes not in competition, ought he, as much as he can, to preserve the rest of mankind, and may not, unless it be to do justice on an offender, take away, or impair the life, or what tends to the preservation of the life, the liberty, health, limb, or goods of another.