Final answer:
American Sign Language (ASL) and Langue des Signes Française (LSF) share a common origin, as ASL was developed using elements from LSF and regional sign languages in the United States.
Step-by-step explanation:
The question asks to identify two sign languages that share a common origin amongst American Sign Language (ASL), British Sign Language (BSL), Langue des Signes Française (LSF), and Nederlandse Gebarentaal (NSL). To determine if two sign languages are related means to find out if they evolved from the same older language. ASL and LSF share a common origin. ASL was developed in part by Thomas Gallaudet and Laurent Clerc in the 19th century, where Clerc brought his knowledge from French Sign Language, the language that LSF is based on, creating a new sign language that incorporated aspects of both LSF and the sign languages that were used regionally in America at that time.