We present two events to study the driving mechanism of extreme-ultraviolet (EUV) waves that are not associated with coronal mass ejections (CMEs), by using high resolution observations taken by the Atmospheric Imaging Assembly (AIA) on board Solar Dynamics Observatory. Observational results indicate that the observed EUV waves were accompanied by flares and coronal jets, but without CMEs that were regarded as the driver of most EUV waves in previous studies. In the first case, it is observed that a coronal jet ejected along a transequatorial loop system at a plane-of-the-sky (POS) speed of 335 ± 22 km s −1 , in the meantime, an arc-shaped EUV wave appeared on the eastern side of the loop system. In addition, the EUV wave further interacted with another interconnecting loop system and launched a fast propagating (QFP) magnetosonic wave along the loop system, which had a period of 200 s and a speed of 388 ± 65 km s −1 , respectively. In the second case, we also observed a coronal jet ejected at a POS speed of 282 ± 44 km s −1 along a transequatorial loop system and the generation of bright EUV wave on the eastern side of the loop system. Based on the observational results, we propose that the observed EUV waves on the eastern side of the transequatorial loop systems are fast-mode magnetosonic waves, and they were driven by the sudden lateral expansion of the transequatorial loop systems due to the direct impingement of the associated coronal jets, while the QFP wave in the fist case formed due to the dispersive evolution of the disturbance caused by the interaction between the EUV wave and the interconnecting coronal loops. It is noted that EUV waves driven by sudden loop expansions have shorter lifetimes than those driven by CMEs.