Thereby and Therefore are both adverbs and serve a similar yet distinct purpose.
Therefore conveys an exact "cause and effect" relationship. Before we can use "therefore," we must state a specific reason in the previous sentence or clause. For example:
I hate being late. Therefore, I always leave my home early to get to my appointments on time.
Therefore = Because of that.
Therefore usually shows up at the beginning of the sentence, while thereby is more frequently used in the middle of a clause.
Thereby also conveys causation, but slightly differently.
The electrons in the foil are heated by the laser pulse, thereby gaining energy.
Thereby = by doing that; through that.
In some cars, the trunk key is broken off right in the lock, thereby jamming it.
Germany will not destroy the euro and thereby endanger the European Union itself.
The residents would be free to leave, though they will thereby forfeit state aid.
I believe that this difference is slightly beyond the College Board's demands in grammar, but being safe is good. If you see a _______ followed by a gerund, it's safe to say you need a thereby.
The rotor is cylindrical and rolls around its axis, thereby catching the current.