In Drosophila melanogaster, the protein Armadillo serves as the homolog of the mammalian β-catenin. This evolutionarily conserved protein plays dual roles in cell-cell adhesion and intracellular signaling pathways that regulate embryonic development.

Armadillo is a key component of adherens junctions, linking the cadherin cell adhesion molecules to the actin cytoskeleton. On the signaling front, Armadillo mediates the Wingless/Wnt pathway, acting as a transcriptional coactivator to govern gene expression patterns essential for segment polarity and proper embryonic patterning.

Mutations in the armadillo gene disrupt both adhesion and signaling functions, resulting in defective segmental patterning during embryogenesis. The functional parallels between Armadillo in Drosophila and β-catenin in vertebrates underscore the conserved nature of developmental signaling pathways across species.

Therefore, the correct homologue of β-catenin in Drosophila is:

(3) Armadillo

Answer: (3) Armadillo