Flagella in eukaryotes and prokaryotes are analogous. Both are a means of moving in an aqueous environment by moving an external projection of the cell. However, the structure of the two kinds of flagella and how they beat is very different. The prokaryotic flagella are rigid and turn due to action inside the cell, while eukaryotic flagella beat by flexing due to internal relative movement of protein filaments.
Work Step by Step
The key here is to see the total difference in how the motion is produced. Such different mechanisms must be analogous, dependent on different proteins, not homologous, dependent on the same proteins.