A coin is flipped 25 times, and we would like to know the probability that 15 or more of those flips are heads side up.

Is it appropriate to use the geometric distribution to calculate probabilities in this situation?

Yes, the geometric distribution is appropriate.
No, since each trial is not independent of the other trials.
No, because it is not looking for the first occurrence of success.
No, since a success and failure on each trial cannot be defined..