Yes, you could say "You should dress properly" or "You should dress appropriately". In the case of going to a fancy dinner, you'd probably end up wearing the same thing either way. However, in general, these sentences are a bit different. There is some overlap between "properly" and "appropriately". They both share a meaning that could make them basically the same, but they also each have a meaning that makes them distinctly different. It's so hard to explain. Haha "Appropriately" means 'in a way that is suitable/right/proper". Appropriate means 'suitable, right, proper'. "Properly" means 'in a way that is suitable/right/proper" or 'in a way that is respectable, decent, refined'. See, proper could mean two things 1) suitable, right, appropriate or 2) respectable, decent, refined; ladylike or gentlemanly. Adding -ly to some adjectives turns them into adverbs mean 'in a _ way'. So depending on which meaning of proper/properly you're using, it could mean essentially the same thing as appropriate/appropriately, or it could be different. "Appropriate" places more emphasis on being correct for the situation, whatever it is (informal or formal). "Proper" emphasizes being respectable and acceptable to society. But it can mean the same thing as "appropriate". Similar yet different! Depends on how it's used! Read and listen to lots of examples!