Why can the crossing of an individual that manifests dominant phenotype with another that manifests recessive phenotype (for the same trait) determine whether the dominant individual is homozygous or heterozygous?

From the crossing of an individual having recessive phenotype with another having dominant phenotype (for the similar trait) it is possible to verify whether the dominant individual is homozygous or heterozygous. This is true because the genotype of the recessive individual is obligatorily homozygous, for instance, aa. If the other individual is also homozygous, AA, the F1 offspring will be only heterozygous (aa x AA = only Aa). If the other individual is heterozygous there will be two dissimilar genotypical forms, Aa and aa in the 1:1 proportion. So if a recessive phenotype appears in the direct offspring the parental individual that manifests dominant phenotype is certainly heterozygous.