Why can 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 the recessive phenotype with another having dominant phenotype (for the same trait) it is possible to determine whether the dominant individual is heterozygous or homozygous. This is true as the genotype of the recessive individual is obligatorily homozygous, for instance, aa. If other individual is also homozygous, AA, the F1 offspring will be only heterozygous (aa x AA = only Aa). If the other individual is the heterozygous there will be two different genotypical forms, Aa and aa in the 1:1 proportion. Thus if a recessive phenotype appears in the direct offspring the parental individual that manifests dominant phenotype is certainly heterozygous.