Final answer:
In mitosis, homologous chromosomes line up independently along the plane of division which ensures that each daughter cell maintains the same number of chromosomes as the parent cell, unlike in meiosis where chromosome number is halved.
Step-by-step explanation:
The arrangement of homologous chromosomes during mitosis is such that each chromosome is lined up independently along the plane of division during metaphase of mitosis. This aligning occurs with the individual chromosomes' kinetochores facing opposite poles. Importantly, the homologous chromosomes do not pair up as they do during meiosis; there is no crossing over in mitosis. The significance of this arrangement is that during anaphase, the sister chromatids are separated and each daughter cell receives one copy of each chromosome, maintaining the same chromosome number as the parent cell. This is in contrast to meiosis, where homologous chromosomes do pair up and crossover, and the chromosome number is halved in the daughter cells as a part of sexual reproduction to form gametes.