(i) Since, transverse waves travel in the form of crests and troughs, they involve changes in the shape of medium. So, they can be transmitted through a medium having elasticity of shape. As solids and liquids have elasticity of shape, hence transverse waves can be transmitted through solids and liquids.
(ii) Since, longitudinal, waves travel in the form of compression's and rare factions, they involve changes in the volume and density of medium. As all media, i.e. solids, liquids and gases have elasticity of volume. Hence, these waves (longitudinal waves) can be transmitted through all the three types of media.