Final answer:
Mendel's work led to the development of the law of segregation, which explains how alleles for a particular trait separate during gamete formation, and is evident in the predictable 3:1 phenotype ratio of offspring. His dihybrid crosses also led to the law of independent assortment, illustrating that alleles for different traits segregate independently.
Step-by-step explanation:
Mendel's work with single-factor crosses resulted in the development of the law of segregation. This law posits that there are two alleles controlling a given characteristic, which separate and go to different gametes when an organism reproduces. As Mendel observed with pea plants, the law of segregation gives rise to genotypic ratios in the F2 generation that can be predicted using a Punnett square. Mendel's experiments showed that when crossing true-breeding pea plants with contrasting traits, the F1 generation would uniformly express the dominant trait, while the F2 generation showed both dominant and recessive traits in a typical 3:1 ratio.
The law of independent assortment, which demonstrates that genes for different traits are passed to offspring independently of one another, was formulated through Mendel's dihybrid crosses. This principle is exemplified by how alleles for seed color and seed texture in pea plants segregate into gametes independently, giving rise to a variety of possible combinations in the offspring.