No one invented the parallelogram*.
If you're asking who discovered or defined the parallelogram, knowledge of parallelograms goes back at least to the ancient Greeks and possibly further. You might be asking something like 'who discovered squares?' or 'who discovered the color yellow?' in that the thing itself existed since the beginning of the universe*, but we've been calling it whatever we call it for longer than history records.
If you asked something like 'who discovered calculus' we could say 'Newton and Leibniz' or if you asked 'who discovered relativitiy' we could say 'Einstein,' but none of those people created calculus / relativitiy / etc..
* depending on your personal beliefs, it might some version of God, Yaweh, Allah, Amenominakanushi, the Flying Spaghetti Monster, or Jack Kirby. But, since we're talking about math and not religion, the working answer is 'no one.'