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We present extinction curves derived from the broad emission lines and continua of samples of 72 radio-loud and 1018 radio-quiet active galactic nuclei (AGNs). The curves are significantly flatter in the UV than curves for the local interstellar medium. The reddening curves for the radio-quiet Large Bright Quasar Survey quasars are slightly steeper than those of the radio-loud quasars in the UV, probably because of additional reddening by dust farther out in the host galaxies of the former. The UV extinction curves for the radio-loud AGNs are very flat. This is explicable with slight modifications to standard Mathis-Rumpl-Nordsieck dust models: there is a relative lack of small grains in the nuclear dust. Our continuum and broad emission line reddening curves agree in both shape and amplitude, confirming that the continuum shape is indeed profoundly affected by reddening for all but the bluest AGNs. With correction by our generic extinction curve, all of the radio-loud AGNs have optical-UV continuous spectra consistent with a single shape. We show that radio-quiet AGNs have very similar intrinsic UV to optical shape over orders of magnitude in luminosity. We also argue that radio-loud and radio-quiet AGNs probably share the same underlying continuum shape and that most of the systematic differences between their observed continuum shapes are due to higher nuclear reddening in radio-selected AGNs and additional reddening from dust farther out in the host galaxies in radio-quiet AGNs. Our conclusions have important implications for the modeling of quasar continua and the analysis of quasar demographics.