Did He teach by Scripture alone? No. The “Scriptures” He taught with were different from the ones in the New Testament, because the New Testament didn’t exist.
Did the Apostles teach by Scripture alone? No. They also taught from the Old Testament because the New Testament did not exist.
It is clear that even the New Testament, when it was compiled was not all encompassing. See the last verse of the last chapter of the Gospel of John.
John 21:25
Jesus did many other things as well. If every one of them were written down, I suppose that even the whole world would not have room for the books that would be written.”
In other words, the Bible doesn’t cover everything.
Paul himself gives a quotation from Jesus that was handed down orally to him: “It is more blessed to give than to receive” (Acts 20:35). This saying is not recorded in the Gospels and must have been passed on to Paul. And therefore Paul himself uses tradition as a guide for teaching.
He also quotes from other non-Biblical sources, such as this early hymn
Ephesians 5:14 for it is light that makes everything visible. This is why it is said: “Wake up, O sleeper, rise from the dead, and Christ will shine on you.”
He says that is authority to teach comes from the lord (1 Thessalonians 4:2)
Paul himself handed on faith…
“For I delivered to you as of first importance what I also received, that Christ died for our sins in accordance with the scriptures. . . . Whether then it was I or they, so we preach and so you believed” (1 Corinthians 15:3,11).
Now I praise you, brethren, that you remember me in all things and keep the traditions as I delivered them to you (I Corinthians 11:2)
“Therefore, brethren, stand fast and hold the traditions which you were taught, whether by word or our epistle”
(II Thessalonians 2:15)
The Ethiopian gives a clue to being ‘taught’ the Word…
Acts 8
30
Then Philip ran up to the chariot and heard the man reading Isaiah the prophet. “Do you understand what you are reading?” Philip asked.
31
“How can I,” he said, “unless someone explains it to me?” So he invited Philip to come up and sit with him.
In other words, he called upon a minister (deacon) to guide him in his readings of the word.
Also, the Ethiopian finds faith, but needs to be baptised (a sacrament).
Acts 10
Cornelius the Roman soldier, finds faith in God, but needs Peter to come to his house before he receives the Holy Spirit. Faith alone was not enough.
In fact, the very name “Acts of the Apostles” not “Faith of the Apostles” tells you something. If faith were alone, then the Bible would have finished at the time Christ rose into heaven; instead it goes on to show what the Apostles did; they taught, they organised, they conferred the gifts of the Holy Spirit upon people.
It is clear that the Ethiopian’s desire to learn was not enough. He had to be taught.
And as I don’t believe in a bible-alone argument, I present as evidence that St. Ignatius, taught by St. Peter himself, and writing before the Bible was compiled wrote…
Epistle to the Ephesians
CHAPTER 5
5:1 For if I in a short time had such converse with your bishop, which was not after the manner of men but in the Spirit, how much more do I congratulate you who are closely joined with him as the Church is with Jesus Christ and as Jesus Christ is with the Father, that all things may be harmonious in unity.
earlychristianwritings.com/text/ignatius-ephesians-lightfoot.html
This reflects the Epistle;
Titus 1:7 Since a bishop is entrusted with God’s work, he must be blameless–not overbearing, not quick-tempered, not given to drunkenness, not violent, not pursuing dishonest gain.