Step 1: Define test cross:
A test cross is a cross between an organism showing the dominant phenotype and a homozygous recessive parent.
The dominant individual may be homozygous (\( \mathrm{TT} \)) or heterozygous (\( \mathrm{Tt} \)). Its look does not tell us which.
The recessive parent (\( \mathrm{tt} \)) is used because it carries only recessive alleles.
Step 2: How the test cross helps:
The recessive parent can give only the \( t \) gamete. So the offspring show which gametes the unknown parent made.
If all offspring are dominant, the unknown parent made only \( T \) gametes. It is homozygous.
If dominant and recessive offspring come in a 1 : 1 ratio, the unknown parent made \( T \) and \( t \) gametes. It is heterozygous.
Step 3: Example with a tall pea plant:
Take a tall pea plant of unknown genotype and cross it with a dwarf plant (\( \mathrm{tt} \)).
Case 1: \( \mathrm{TT} \times \mathrm{tt} \) gives all \( \mathrm{Tt} \), so all plants are tall.
Case 2: \( \mathrm{Tt} \times \mathrm{tt} \) gives \( \mathrm{Tt} \) and \( \mathrm{tt} \) in equal numbers, so tall : dwarf is 1 : 1.
So the ratio of the progeny reveals the genotype of the tall plant.
Final Answer:
A test cross is a cross of a dominant-phenotype individual with a homozygous recessive. All dominant offspring show the unknown parent is \( \mathrm{TT} \). A 1 : 1 ratio shows it is \( \mathrm{Tt} \).