You were born on the cusp. The cusp is the dividing line between two signs. You are aware that the planets are constantly moving and that is why charts must be drawn up, because the planetary positions are never the same on the same dates.
Hence, the dividing line between Sag is Dec. 20 & 21st. You have to have a chart done to see what position Sagittarius was in for your birth year. I don't know an awful lot about it but I do know that much.
I posted another post about it but do an internet search for Free Natal Horoscope. Find one you like that looks legit. Some give you a free analysis and some don't. You enter your DOB, time, and place of birth and it almost instantly gives you your full chart. Then save it/them to your hard drive in a special file. It's nice to have.
My favorite report is "Thank you for visiting the Astrolabe WEB site at
http://alabe.com " Another nice analysis came from CafeAstrology.com. I cannot vouch for the accuracy of any of these.