I've had a few experiences with muslims in the past and even recently encountered one in Christian Chat. There are similarities up to a point. Both religions believe they serve the God of Abraham and that Abrahams son was the recipient of God's covenant. God promised to give Abraham a son, an heir. Abraham and Sarah doubted this and so Sarah gave Abraham their maid/servant and the servant woman (named Hagar), became pregnant and had a son named Ishmael. The arabic nations are descended from Ishmael and the religion of islam believes and teaches that Ishmael was the promised/blessed son.
The reason they believe this is because when Sarah began to despise Hagar (the servant woman), Hagar was told to leave their home by Abraham. She was found by God crying in the wilderness and she had left the child, (Ishmael) to die. God heard the child's crying and spoke to Hagar, he said he would bless Ishmael and that twelve princes would be in his lineage. Muslims believe that because God said this, at the time that he comforted Hagar, that they are the chosen nation of God and that the Jewish people are not. Jesus was also from Isaacs family line, and you will find throughout scripture that God established his covenant with Isaac, Abraham and Sarah's son.
In Genesis 17:21 It says, "But my covenant I establish with Isaac, shom Sarah will bear to you at this time next year".
You'll find some of the story of Hagar and Ishmael in Genesis chapter 16.
Many muslims will acknowledge Jesus existence and even his crucifixion, but will not acknowledge that He is the savior of the world and that only through Him, can we have eternal life.
