Final answer:
The correct behavior of medium particles in a transverse wave is perpendicular oscillation to the direction of wave propagation without following the wave.
Step-by-step explanation:
The statement that best describes how the particles of a medium behave when a transverse wave moves through the medium is: Particles move perpendicular to the direction of the wave as the wave passes through them, but do not move along with the wave. In a transverse wave, the motion of the particles of the medium is perpendicular (at a right angle) to the direction of propagation of the wave. Therefore, if a transverse wave is traveling from left to right, the particles of the medium would oscillate up and down.