How did third-generation pea plants help Gregor Mendel test his conclusions?

Gregor Mendel used the third generation (F₃) of pea plants to experimentally verify his hypotheses regarding the genotype of plants that displayed dominant traits.1

While F₂ plants showing a dominant trait (such as purple flowers) appeared identical, Mendel knew they could be either homozygous (RR) or heterozygous (Rr). By raising an F₃ generation from these dominant-phenotype plants, he could test their genetic makeup:

• Verification of Segregation: Mendel predicted that approximately two-thirds of the purple-flowered F₂ plants were actually heterozygotes. He confirmed this by observing that these plants produced offspring with the recessive white-flower trait in the F₃ generation, proving the presence of the hidden recessive allele in the parent's genotype.1
• Testing Independent Assortment: When studying multiple traits, such as seed color and shape, Mendel used the F₃ generation to confirm the existence of nine different genotypes among the four phenotypic classes observed in the F₂ generation.1

By observing these specific ratios in the F₃ generation, Mendel provided empirical evidence for his law of segregation and law of independent assortment.1