Two of the best-known stories about Abraham are not in Genesis at all, and tracing where they are found says a good deal about how traditions grow around a founder.
The first is the smashing of the idols. Genesis says nothing of Abraham's youth; the story in which the young man destroys the idols in his father Terah's shop, leaves the axe in the hand of the largest, and then mocks his father's protest that statues cannot act, comes from rabbinic midrash, Genesis Rabbah, filling the silence about how a man raised among idolaters came to one God. The Quran tells a version directly (Sura 21): Ibrahim breaks the idols, argues with his people, and is thrown into a fire that God commands to be cool and safe for him. Later tradition names the king who casts him in as Nimrod.
The second belongs to Islam alone. The Quran has Ibrahim and his son Ishmael raise the foundations of the Kaaba at Mecca, praying that God accept it, and Islamic tradition connects to the same family the well of Zamzam that saved Hagar and the infant Ishmael, and the maqam Ibrahim, the station of Abraham, near the shrine. The rites of the Hajj are understood as retracing the acts of Abraham, Hagar and Ishmael, which places Abraham not at the origin of a rival lineage but at the physical centre of Muslim worship.
The figure the three faiths share is thus elaborated quite differently in each, and the differences are not incidental but load-bearing.