The is only One source of Truth, God the Father has revealed and is unfolding the mysteries of faith thought his Son in the Spirit. This process takes place within the Living Church which is the body of Christ. The teaching authority of the Church unfolds the mysteries of faith by using both Tradition and Scripture. The New Testament itself demonstrate the process of living tradition.
Tradition is the process through which "the Church, in her doctrine, life and worship, perpetuates and transmits to every generation all that she herself is, all that she believes."(Cath. of Cath Church, #76)
Scripture consists or the writings of the inspired Apostles and Evangelists who wrote the four gospels, letters and events of the early Church history.
These two sources of faith, Sacred Tradition and Sacred Scripture, are bound closely together and communicate with one another because both of them spring from the same divine source and move together toward the same divine end. Each of them in its own way makes present the mystery of Christ. (Cath. of Cath Church, #79) We see this at work in the definition of the Assumption.
In Scripture Mary is declared by the angel Gabriel as full of grace because she was to be the dwelling place of God's Son and she realized that all generations would call her Blessed because God had done great things for her. The truth of the Assumption is not explicitly found in Scripture so the Pope had to rely heavily on tradition.
Pope Pius XII in 1950 defined the truth of the Assumption of Mary into heaven with body and soul. The Pope in his encyclical "Munificentissimus Deus" defining the Assumption indicates the reasons why he did so.
1. The increasing number of petitions coming from all over the Catholic world asking for the definition of the Assumption.
2. The "Fathers of the Vatican Council, urgently petitioned the Apostolic See to this effect."
3. The many theological investigations pointing out that this was contained in the deposit of faith.
4. He addressed to each bishop the following question: "Do you venerable brethren, in your understanding wisdom and prudence judge that the bodily assumption of the Blessed Virgin can be proposed and defined as a dogma of faith? Do you, with your clergy and people, desire it?" The bishops gave an almost unanimous answer, "Yes".
5. Innumerable Churches had bee dedicated to the Virgin Mary Assumed into heaven.
6. Images of the Assumption were exposed to the veneration of the faithful.
7. The number of cities and dioceses placed under the special patronage and guardship of the Virgin Assumed into heaven.
8. The Byzantine liturgy celebrated the Dormition as follows: "God, the King of the universe, has granted you favors that surpass nature. As he kept you a virgin in childbirth, thus he has kept your body incorrupt in the tomb and has glorified it by his divine act of transferring it from the tomb."
9. Fathers and great doctors of the Church in their homilies and sermons spoke of this doctrine as something already known and accepted by Christ's faithful.
10. A number of great Saints who asserted the truth of the Assumption.
The Scholastic Doctors recognized the Assumption in the figure of the Ark
of the Covenant and as the Woman clothed with Sun in the book of Revelation.
12. "The Church never looked for the bodily relics of the Blessed Virgin Mary nor proposed them for the veneration of the people." Why not?
13. Finally, the Assumption was the logical conclusion to Mary's life which had been defined as "Mother of God" and the "Immaculate Conception.'
As you can see, the Pope Pius XII relied heavily on Tradition but did not disregard Scripture in which this truth is contained implicitly.