How is the Declaration of Independence similar to the u. s. constitution?

Their connection is not difficult to understand.

The Declaration is a statement based on natural law. Natural law consists of fundamental principles of justice and right. Monotheists see natural law as deriving from the Creator. Polytheists see it as deriving from the supreme deity or deities. Atheists who believe in natural law, such as the late philosopher/novelist Ayn Rand, view it as a collection of rules inherent in the way the universe works.

Both were inspired by ideas popularized during the Enlightenment.