The word "祖祠" is formed by combining the character "祖", meaning ancestor, which incorporates the radical "示" related to worship and the component "且" historically associated with an altar, with the character "祠", meaning temple, which combines the radical "示" for worship and the phonetic component "司" indicating pronunciation. Together, they create a compound word where "祖" specifies the ancestral focus and "祠" denotes the place of worship, resulting in the meaning of ancestral temple.