I believe that Bigfoot can be explained much like dragons can. Someone came across some strange bones at one point in time, and since they had no concept of fossils, extinction or evolution, they thought the creature must be real and the bones were of just an unfortunate specimen that recently died.

Gigantopithecus was part of the Australopithecus linewhich were very real. They were huge, much larger than us with skull comparable with modern gorillas.