Sponsored search auction is a crucial component of modern search engines. It requires a set of candidate bidwords that advertisers can place bids on. Existing methods generate bidwords from search queries or advertisement content. However, they suffer from the data noise in <query, bidword> and <advertisement, bidword> pairs. In this paper, we propose a triangular bidword generation model (TRIDENT), which takes the high-quality data of paired <query, advertisement> as a supervision signal to indirectly guide the bidword generation process. Our proposed model is simple yet effective: by using bidword as the bridge between search query and advertisement, the generation of search query, advertisement and bidword can be jointly learned in the triangular training framework. This alleviates the problem that the training data of bidword may be noisy. Experimental results, including automatic and human evaluations, show that our proposed TRIDENT can generate relevant and diverse bidwords for both search queries and advertisements. Our evaluation on online real data validates the effectiveness of the TRIDENT's generated bidwords for product search.