Sponsored search auction is crucial for commercial search engine, which heavily relies on the bidwords generated from search queries and advertisements. However, current bidword generation models suffer from the noisy and data due to the keyword bidding problem. In this paper, we propose a triangular bidword generation model (TRIDENT), which takes the high-quality data of paired 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 triangle 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. Additionally, an online evaluation is simulated to further validate that the generated bidwords can be correctly recommended to relevant products.