Prophecies
Jesus fulfilled all the prophecies concerning the messiah uttered by the prophets under the old covenant (in the Old Testament).
Jesus' birth
The phophet Isaiah prophesied that a virgin would give birth to the messiah.
Mary was a virgin when Jesus Christ was conceived of the Holy Spirit in her womb. Joseph wanted to break up with her.
But while he thought about these things, behold, an angel of the Lord appeared to him in a dream, saying, "Joseph, son of David, do not be afraid to take to you Mary your wife, for that which is conceived in her is of the Holy Spirit." (Matthew 1:20, NKJV).
The prophet Micah prophesied that the messiah would come forth from Bethlehem of Judea.
Jesus was born in Bethlehem of Judea in the days of Herod the king, as Joseph of the lineage of David had to be registered with Mary in Bethlehem because of the census decreed by Caesar Augustus;
But you, Bethlehem Ephrathah, Though you are little among the thousands of Judah, Yet out of you shall come forth to Me The One to be Ruler in Israel, Whose goings forth are from of old, From everlasting. (Micah 5:2, NKJV).
The prophet Isaiah announced the birth of the son of God:
For unto us a Child is born, Unto us a Son is given; And the government will be upon His shoulder. And His name will be called Wonderful, Counselor, Mighty God, Everlasting Father, Prince of Peace. (Isaiah 9:6, NKJV)
The prophet Hosea predicted the events after Jesus was born.
After Jesus' birth, Joseph, Mary and the baby Jesus went to Egypt to flee King Herod who wanted to kill the child. They returned to Galilee after he died. "And out of Egypt I called My son." (Hosea 11:1-b, NKJV)
Jesus' ministry
Jesus said that he came to do his Father's will.
Jesus fulfilled Isaiah's prophecy concerning the savior.
Jesus Christ read the prophecy of Isaiah to the Jews in the synagogue:
The Spirit of the Lord GOD is upon Me, Because the LORD has anointed Me To preach good tidings to the poor; He has sent Me to heal the brokenhearted, To proclaim liberty to the captives, And the opening of the prison to those who are bound; To proclaim the acceptable year of the LORD, And the day of vengeance of our God; To comfort all who mourn. (Isaiah 61:1-2, NKJV).
The sufferings of Christ
The prophet Isaiah predicted the sufferings of Christ and his death in order to atone for the sins of men (men : means men and women).
He is despised and rejected by men, A Man of sorrows and acquainted with grief. And we hid, as it were, our faces from Him; He was despised, and we did not esteem Him. Surely He has borne our griefs And carried our sorrows; Yet we esteemed Him stricken, Smitten by God, and afflicted. But He was wounded for our transgressions, He was bruised for our iniquities; The chastisement for our peace was upon Him, And by His stripes we are healed. (Isaiah 53:3-5, NKJV)
Jesus was raised from the dead
David predicted Jesus Christ's resurrection. David spoke of Christ when he said that his soul would not be abandoned:
"For You will not leave my soul in Sheol, Nor will You allow Your Holy One to see corruption. You will show me the path of life; In Your presence is fullness of joy; At Your right hand are pleasures forevermore." (Psalm 16:10-11, NKJV).
David died and was buried with his ancestors, whereas Jesus Christ was raised from the dead as Paul testified about it:
For David, after he had served his own generation by the will of God, fell asleep, was buried with his fathers, and saw corruption; but He whom God raised up saw no corruption. Therefore let it be known to you, brethren, that through this Man is preached to you the forgiveness of sins; and by Him everyone who believes is justified from all things from which you could not be justified by the law of Moses. (Acts 13:36-39, NKJV).