Why does church tradition teach that one third of the angels fell with Lucifer when no verse supports that

Yes, you are right to conclude that you must include the other books o the Bible, to discern what Jesus said. We cannot actually see spirit creatures in their natural form, including Jesus and God. It is pretty evident that 1/3 of the stars mean the wicked angels that were kicked out of heaven. The Bible warns of the things that would follow on the Earth after being kicked out of Heaven. From King James: Therefore rejoice, ye heavens, and ye that dwell in them. Woe to the inhabiters of the earth and of the sea! for the devil is come down unto you, having great wrath, because he knoweth that he hath but a short time.” This of course is why things on the Earth are so bad!

Your assertion that the emergence of the woman in 12:1 takes place during the tribulation does not appear to be correct, in light of these two verses taken together;

Revelation 1:19 KJV Write the things which thou hast seen, and the things which are, and the things which shall be hereafter;

According to this scripture, the Revelation is divided into three distinct sections. Those three are; the things you have seen, those that are, and those yet to come.

Revelation 11:19 KJV  And the temple of God was opened in heaven, and there was seen in his temple the ark of his testament: and there were lightnings, and voices, and thunderings, and an earthquake, and great hail.

notice that the command to write states have seen, which designates writing at a future date and not at the present; otherwise it would say what you see rather than have seen.

In verse 11:19 begins the opening of visions of the past. Verse 19 comes at the end of the seventh trumpet judgment.

Revelation 11:15 through 18 And the seventh angel sounded; and there were great voices in heaven, saying, The kingdoms of this world are become the kingdoms of our Lord, and of his Christ; and he shall reign for ever and ever.  And the four and twenty elders, which sat before God on their seats, fell upon their faces, and worshipped God, Saying, We give thee thanks, O Lord God Almighty, which art, and wast, and art to come; because thou hast taken to thee thy great power, and hast reigned. And the nations were angry, and thy wrath is come, and the time of the dead, that they should be judged, and that thou shouldest give reward unto thy servants the prophets, and to the saints, and them that fear thy name, small and great; and shouldest destroy them which destroy the earth. 

beginning with the vision: in 12:1 what we have is a summary of the charges against Satan and the fallen angels all of which took place prior to creation. We know this because;

Revelation 12:17  And the dragon was wroth with the woman, and went to make war with the remnant of her seed, which keep the commandments of God, and have the testimony of Jesus Christ.

These events are referred to in the past tense. notice and went to make war with her seed, and not will go. We have further evidence that these events are in the past due to:

Luke 10:18  And he said unto them, I beheld Satan as lightning fall from heaven. 

These words of Jesus were uttered 2000 years ago and if it was past then it was surely past when John had his vision.

The Revelation is difficult to understand unless we include the rest of the Bible in discerning what Jesus said.

Hope this helps.  

@BYE points in the right direction. Some of the prophecies in Revelation look backwards to events that occurred before John lived, because the contest between Satan and God goes back to the beginning of the world.

12 A great sign appeared in heaven: a woman clothed with the sun, with the moon under her feet and a crown of twelve stars on her head. 2 She was pregnant and cried out in pain as she was about to give birth. 3 Then another sign appeared in heaven: an enormous red dragon with seven heads and ten horns and seven crowns on its heads. 4 Its tail swept a third of the stars out of the sky and flung them to the earth. (Revelation 12:1-4)

Verse four is interpreted by some to represent angels as stars. Thus the stars that fall to the earth are fallen angels, and they number one third of all stars, hence one third of all angels.

Jamieson-Fausset-Brown Bible Commentary

4. drew—Greek, present tense, "draweth," "drags down." His dragging down the stars with his tail (lashed back and forward in his fury) implies his persuading to apostatize, like himself, and to become earthy, those angels and also once eminent human teachers who had formerly been heavenly (compare Re 12:1; 1:20; Isa 14:12).

This commentary considers several possible meanings, including the stars being angels or martyred Christians.

Expositor's Greek Testament

Revelation 12:4. The symbolism is a reminiscence of an ætiological myth in astrology (cf. the cauda of the constellation Scorpio) and of the primitive view which regarded the dark cloud as a snake enfolding the luminaries of heaven in its hostile coils (Job 3:8; Job 26:13, with A. B. Davidson’s notes). Thus the Iranians (S. B. E. iv. p. lxxiii., Darmesteter) described the fiend as a serpent or dragon not on the score of craftiness but “because the storm fiend envelops the goddess of light with the coils of the cloud as with a snake’s fold”. The same play of imagination would interpret eclipses and falling stars, and, when the pious were compared to stars (as in Egyptian theology, Plut. de Iside, 21), it was but a step to the idea of Daniel 8. (cf. Sib. Or. ver. 512 f., the battle of the stars), where Antiochus Epiphanes does violence to some devout Israelites who are characterised as stars flung rudely down to earth (i.e., martyred, 1 Maccabees 1.) Originally, this description of the dragon lashing his tail angrily and sweeping down a third of the stars probably referred to the seduction of angels from their heavenly rank (so 8–9) to serve his will (Weiss). But John, in recasting the tradition, may have thought of the Danielic application, i.e., of the devil succeeding in crushing by martyrdom a certain number of God’s people. In this event, they would include at least, if they are not to be identified with, the pre-Christian martyrs of Judaism (cf. Hebrews 11:32 f. Matthew 23:35).—ἕστηκεν, a conventional posture of the ancient dragon cf. e.g., Pliny, H. N. viii. 3, “nec flexu multiplici ut reliquae serpentes corpus impellit, sed celsus et erectus in medio incedens”; ibid. viii. 14, for serpents devouring children. The mother of Zoroaster had also a vision of wild beasts waiting to devour her child at its birth. This international myth of the divine child menaced at birth readily lent itself to moralisation, or afforded terms for historical applications, e.g., the abortive attack on Moses, the prototype of messiah (Baldensperger, 141, 142) at his birth (Acts 7:20 f.) and the vain efforts of Herod against the messiah. The animosity of Pytho for Leto was due to a prophecy that the latter’s son would vanquish him.

This commentary also agrees that the stars are angels:

Pulpit Commentary

Verse 4. - And his tail drew the third part of the stars of heaven, and did cast them to the earth; draweth (Revised Version). Not the stars with which the woman is crowned (see ver. 1), but other stars. In describing the vast power of the devil, St. John seems to allude to the tremendous result of his rebellious conduct in heaven, in effecting the fall of other angels with himself (Jude 1:6).