Answer:
The three documents were beacons of light that gave two major things, freedom and security. More specifically, the Declaration of Independence and the Declaration of Rights to Man gave freedom and The Constitution gave security.
The two declarations gave the people freedom to do as they wished. It allowed people to pursue the things they wanted without government intervention. It also gave the right to religion and the right to speech. This granted individuals the ability to seek happiness by any means that is not hindered by law. The Constitution worked in tandem with the declarations, allowing more secure freedom. The Constitution acted as the universal law of man, giving people the right to bear arms and the right to be treated fairly by both law and court.
All three of those documents granted safety and liberty among the people it applied to. However, safety and liberty were not values that were always available to people from different countries. This was so much so that safety and liberty became commodities, and as the influence of the three documents spread, those same commodities became the motivation for thousands of people to revolt. These insurrections required leaders who would be able to spearhead and guarantee that the revolutions would succeed. This allowed the rise of people like Simon Bolivar and Jose de San Martin. These two people were some of the most historically significant leaders of the South American Revolutions. However, every leader needed ideals to follow, and these ideals were heavily entrenched with the theories of liberty and liberal thought.
These same ideals were heavily prevalent after the revolutions succeeded. To ensure that tyrannical rule would be eradicated, the leaders constructed a declaration of their own. This was called The Venezuelan Declaration of Independence. The ideal that was prevalent was the idea of equality and fairness that was present in the American documents. The Venezuelan Declaration of Independence granted the freedoms and safety of the individuals that it applied to, similar to the American documents.