Final answer:
The offspring's genetic disorder is caused by recessive inheritance, where the parents passed down harmful recessive genes from the same lineage.
Step-by-step explanation:
The process that contributed to the offspring's genetic disorder is known as recessive inheritance. Recessive inheritance occurs when an individual inherits two copies of a recessive gene, one from each parent.
In this case, both parents carried harmful recessive genes passed down from the same lineage. If both parents transmit their abnormal allele to the offspring, it can result in the development of a genetic disorder.
An example of a genetic disorder caused by recessive inheritance is Tay-Sachs disease, where the offspring inherits two copies of the faulty allele and develops the disease.