To determine the most likely genotypes of the parents that result in 100 percent heterozygous offspring for the trait of plant height, let's analyze each potential cross mentioned:
1. Cross: [tex]$Tt \times tt$[/tex]
- One parent is heterozygous ([tex]$Tt$[/tex]), and the other parent is homozygous recessive ([tex]$tt$[/tex]).
- The possible offspring from this cross would be:
- [tex]$Tt$[/tex] (from T from the first parent and t from the second parent)
- [tex]$tt$[/tex] (from t from both parents)
- The genotypes of the offspring: [tex]$Tt$[/tex] and [tex]$Tt$[/tex].
- Since all offspring (100%) are heterozygous ([tex]$Tt$[/tex]), this cross is a suitable candidate.
2. Cross: [tex]$Tt \times Tt$[/tex]
- Both parents are heterozygous ([tex]$Tt$[/tex]).
- The possible offspring from this cross would be:
- [tex]$TT$[/tex] (from T from both parents)
- [tex]$Tt$[/tex] (from T from one parent and t from the other parent)
- [tex]$Tt$[/tex] (from t from one parent and T from the other parent)
- [tex]$tt$[/tex] (from t from both parents)
- The genotypes of the offspring: [tex]$TT$[/tex], [tex]$Tt$[/tex], [tex]$Tt$[/tex], and [tex]$tt$[/tex].
- The ratio would be approximately 1:2:1 (25% [tex]$TT$[/tex], 50% [tex]$Tt$[/tex], 25% [tex]$tt$[/tex]), so not all offspring would be heterozygous. This cross cannot result in 100% heterozygous offspring.
3. Cross: [tex]$tt \times tt$[/tex]
- Both parents are homozygous recessive ([tex]$tt$[/tex]).
- The possible offspring from this cross would be:
- [tex]$tt$[/tex] (from t from both parents)
- The genotypes of the offspring: [tex]$tt$[/tex].
- Since all offspring (100%) are homozygous recessive, not heterozygous, this cross is incorrect for the given condition.
4. Cross: [tex]$\pi \times t t$[/tex]
- The genotype [tex]$\pi$[/tex] is not a valid genotype in genetics. This suggestion appears to be erroneous or unrelated to standard genetic notation.
- Thus, we can disregard this option.
From the analysis above, the cross that results in 100% heterozygous ([tex]$Tt$[/tex]) offspring is:
[tex]$Tt \times tt$[/tex].
Therefore, the most likely genotypes of the parents are:
[tex]\[ \boxed{Tt \times tt} \][/tex]
