How are the ten commandments reflected in American laws?

You shall not murder. Murder, obviously, is illegal.


You shall not commit adultery
In several states, predominately southern states, adultery is still illegal.

You shall not steal.
Some states call this Theft by Taking, Conversion, Deception, etc... Some states call it Larceny.

You shall not bear false witness against your neighbor. This can be construed as both False Report of a Crime and as Perjury. Either will apply if you supplied police with a suspect when you falsely reported a crime.

Answer

The ten commandments are not old enough nor comprehensive enough to claim a place in the sources for modern US law. The well documented history of US law traces its roots to English common law which traces its roots to the Magna Carta.

Hammurabi was the ruler in Babylon from 1792-1750 BCE. His code was the precursor to Hebrew law. The Code of Hammurabi is estimated to predate the Ten Commandments by 500-1000 years. Hammurabi's Code is an extremely comprehensive system of law that showed his commitment to protect the weak from the strong and mete out justice for all. It was much more comprehensive than the Ten Commandments which are quite simplistic in their subject matter.

Hammurabi's Code addressed hundreds of civil and criminal legal infractions. It is interesting to note that it addressed women's rights to a degree that didn't appear in the Western World until the nineteenth and early twentieth centuries. Woman enjoyed a separate legal existence in Hammurabi's reign over 3700 years ago. Hammurabi's Code addressed civil life for all the citizens while the ten commandments are heavily influenced by mandates regarding religious worship. In fact, the first four commandments are unconstitutional. You can look through the Code of Hammurabi at the related link.

The Magna Carta was compiled in 1215 CE and was written as a declaration that the people who lived under the rule of a monarch had basic political and civil rights, as landowners, that limited monarchal authority which had previously been absolute.

The Magna Carta was the basis for constitutional law in the Western World. Some clauses are still in use today in various legal systems. The Magna Carta led to the development of English common law which forms the basis for law in the United States. Both the Magna Carta and English common law were brought to the New World by English settlers.