Stalactites hang from the ceilings like tights from a washing line, and stalagmites just MIGHT reach the ceiling!
They hang from the top of a cave downwards, not from the bottom upwards, that would be a stalagmite.
Just to help remember the difference, think "s-t-a-l-a-C (celing)-t-i-t-e" and "s-t-a-l-a-G (ground)-m-i-t-e." StalaCtite comes down from the celing. StalaGmite grows up from the ground. :)
When I was a teenager at school the difference was explained to us as being; "Tights come down, and the Mites go up!"
A stalactite (Greek stalaktites, (Σταλακτίτης), from the word for "drip" and meaning "that which drips") is a type of speleothem (secondary mineral) that hangs from the ceiling or wall of limestone caves. It is sometimes referred to as dripstone.