Why assume I havent' read the Bible? Islam is the old testement without the compassion and redemption of the new. But the God of the old testement is also the exact same God of the New testement this you can not deny. God did not change His nature with the birth of Jesus, only our understanding of Him changed. Since the Jewish and Muslim religions also share the same core then they worship the same God, only without the better understanding that Christianity provides.
Like I say, if you deny the God of Christians is not the God of Islam then the God of Christians can't be the God of the Jews, and the God of Catholics can't be the God of the baptists and the god of the Baptists can't be the God of the methodists and the god of the methodists can't be the God of the Mormons. The fact is, HE is in all of these religions, only his messagers have changed.