You are studying reproduction in a species of frog. Two gametes that are each diploid join to form a viable zygote (F1). If the F1 mates with one of the parents will there be viable offspring?

No, viable offsprings will not be formed.

Explanation:

Viable offsprings will only be formed if both the organisms which are mating have haploid sex chromosomes. Sexual reproduction is the process by which two haploid cell i.e  the haploid egg and haploid sperm, fuse to form the zygote. However, if two diploid cells will join to form a zygote then the number of chromosomes in the daughter cell will not be maintained. Such a daughter cell will be different completely from the parent cell.

a unit of heredity that is transferred from a parent to offspring and is held to determine some characteristic of the offspring.