Final answer:
The statement is true as waves' amplitudes add up due to constructive interference when they propagate in the same line. Constructive interference leads to a larger resultant wave amplitude.
Step-by-step explanation:
The statement "The amplitudes of waves add up only if they are propagating in the same line" is indeed true. This phenomenon is a result of constructive interference, which occurs when two or more waves overlap and their displacements are in the same direction—effectively consolidating their energy and creating a resultant wave with a larger amplitude. However, if the waves are not propagating along the same line or in phase with each other, they may not add up constructively and could result in destructive interference, where their combined amplitude could decrease or they may even cancel each other out.