Euclid's fifth postulate:
If a line segment intersects two straight lines forming two interior angles on the same side that sum to less than two right angles, then the two lines, if extended indefinitely, meet on that side on which the angles sum to less than two right angles.
Every example (that I've seen) of proving that the parallel postulate in Euclid's five postulates is independent of the others seems to rely on the fact that one can invent a new kind of geometry where the first four postulates hold without the existence of the parallel postulate. Hyperbolic and elliptic geometry are often used as examples. Is this the only known method or approach to prove the parallel postulate's independence? Is discovering these curved geometries as counterexamples the only way?