Before Jesus was born, the religious leaders of Israel had already decided what it meant to live righteously. They had developed a system contrary to Scripture based on self- righteousness generated by doing good works. When Jesus entered the world, He shattered their religious system by upholding the standard revealed in God's Word. He revealed how a citizen of His Kingdom really lives.
If you want to know if you're a Christian, compare your life with the standard Christ presents in the Sermon on the Mount. One word summarizes His standard: righteousness. Examine the lives of many professing Christians, and you'll find no such righteousness. Someone once told me about a woman who said she was a Christian but was living with a man who was not her husband. First Corinthians 6:9 says that those characterized by sexual immorality ("fornicators" "shall not inherit the kingdom of God ." That woman was living in a state of unrighteousness. But righteousness characterizes true conversion.
Matthew 5:20, the key verse in the Sermon on the Mount, says, "Except your righteousness shall exceed the righteousness of the scribes and Pharisees, ye shall in no case enter into the kingdom of heaven." The scribes and Pharisees went to the Temple regularly, paid tithes, fasted, and prayed constantly. But Christ wasn't impressed with their religious performance. He said no one would enter His Kingdom whose righteousness didn't exceed theirs. Righteousness—living by God's standards—is what sets a person apart as God's child.