Faults in complex tectonic environments interact in various ways, including triggered rupture of one fault by another, that may increase seismic hazard in the surrounding region. We model static and dynamic fault interactions between the strike-slip and thrust fault systems in southern California. We find that rupture of the Sierra Madre-Cucamonga thrust fault system is unlikely to trigger rupture of the San Andreas or San Jacinto strike-slip faults. However, a large northern San Jacinto fault earthquake could trigger a cascading rupture of the Sierra Madre-Cucamonga system, potentially causing a moment magnitude 7.5 to 7.8 earthquake on the edge of the Los Angeles metropolitan region.