According to some scholars, they think Matthew might have been written before Mark, or at possibly the same time.
It's interesting how you call it plagiarizing, when in fact, if they both were around, they would have both seen the same things. That would account for many of the similarities. (if 3 people attend a football game and 1 of the 3 is rooting for the losing team, the stories of the two that were rooting for the winning team could be similar, though, the story of the losing team, will probably be told in a different view). So if Matthew, Mark(who never said he didn't see Jesus, we just have no evidence to suggest he did), and Luke all saw the sermon's that Jesus taught, that would explain the quotes of what Jesus said.
Many scholars suggest that Mark was a friend of Peter's, but no timetable is given to how long they were friends, or whether Mark ever even saw Jesus, so most arguments about Mark, are un-provable either way.
And even using the latest date John wrote his Gospel, which would be around 55 years after the death of Jesus, would put him at approximately 75-85 years old when he wrote it, thus he could be a contemporary of Jesus.