Wave-particle complementarity is one of the most intriguing features of quantum physics. To emphasize this measurement apparatus-dependent nature, experiments have been performed in which the output beam splitter of a Mach-Zehnder interferometer is inserted or removed after a photon has already entered the device. A recent extension suggested using a quantum beam splitter at the interferometer's output; we achieve this using pairs of polarization-entangled photons. One photon is tested in the interferometer and is detected, whereas the other allows us to determine whether wave, particle, or intermediate behaviors have been observed. Furthermore, this experiment allows us to continuously morph the tested photon's behavior from wavelike to particle-like, which illustrates the inadequacy of a naive wave or particle description of light.