Final answer:
The falcon-headed god who avenged the murder of his father, Osiris, by defeating Seth, is Horus. Horus is associated with the sky, kingship, and the cycle of life and death, symbolizing the power and protection offered by the reigning Pharaoh in ancient Egypt.
Step-by-step explanation:
The falcon-headed god who was the son of Osiris and avenged his father's death by hunting down his murderer, Seth, is none other than Horus. Horus is a significant deity in Egyptian mythology, representing the sky and kingship. His father, Osiris, the lord of the underworld, was killed by his brother Seth, the god of chaos and the desert. Osiris's wife, Isis, using her magical powers, resurrected Osiris long enough for them to conceive Horus. Horus grew to challenge and defeat Seth, establishing himself as the rightful ruler and protector of the land.
According to the myth, Osiris ruled the realm of the dead, and his story is tightly connected with the Nile's annual flooding, reflecting the cycle of death and rebirth. Ancient Egyptians viewed Horus as the embodiment of the living Pharaoh and also believed in the afterlife blessings from a just Osiris to those who lived a righteous life. Artistic representations of Horus typically showcased the sky god with a falcon's head, symbolizing his dominion over the sky.