State-of-the-art question answering (QA) systems employ term-density ranking to retrieve answer passages. Such methods often retrieve incorrect passages as relationships among question terms are not considered. Previous studies attempted to address this problem by matching dependency relations between questions and answers. They used strict matching, which fails when semantically equivalent relationships are phrased differently. We propose fuzzy relation matching based on statistical models. We present two methods for learning relation mapping scores from past QA pairs: one based on mutual information and the other on expectation maximization. Experimental results show that our method significantly outperforms state-of-the-art density-based passage retrieval methods by up to 78% in mean reciprocal rank. Relation matching also brings about a 50% improvement in a system enhanced by query expansion.