Final answer:
Homologous chromosomes pair up during both prophase I and metaphase I of meiosis I, which allows genetic recombination and proper segregation of chromosomes.
Step-by-step explanation:
Homologous chromosomes are paired during both prophase of meiosis I and metaphase of meiosis I. During prophase I, homologous chromosomes pair up, which is a unique event in meiosis, characterized by processes such as crossing-over and synapsis. This pairing is critical for the alignment of chromosomes so that genetic recombination can occur. The pairing is evident as the chromosomes are connected by a lattice of proteins and attach at their tips to the nuclear envelope before it breaks down. In metaphase I, the paired homologous chromosomes line up in the middle of the cell, prepared for their segregation into separate gametes.
In contrast, during prophase of meiosis II and metaphase of meiosis II, homologous chromosomes do not pair. Instead, sister chromatids are aligned during metaphase II in preparation for their separation into gametes, ensuring that each gamete ends up with a single set of chromosomes.
Therefore, the final answer in 20 words: Homologous chromosomes are paired during both prophase I and metaphase I of meiosis.