It was fortunate that their research interests coincided.

coincided 是动词 coincide 的过去式。coincide 由前缀 co-（表示"共同"）和词根 -incide（来自拉丁语 incidere，意为"落下、发生"）组成，字面意思是"同时发生"，引申为"一致、相符"的意思。