olars have concluded that Luke's special source--L--was faithfully utilized in the Gospel of Luke. See Kim Paffenroth, The Story of Jesus According to L; Robert E. Van Voorst, Jesus Outside the Gospels, page 136-143. Indeed, "[a]lthough there are minor changes, there is no evidence that Luke has invented material not found in his sources. Indeed, the gospel as a whole shows no evidence of such a tendency, and in view of this it is a fair assumption that he would not have resorted to it in the continuation in Acts." Donald Guthrie, New Testament Introduction, page 380.
In sum, when evaluating the speeches in Acts, "we have to reckon with the demonstrable factor that Luke used sources for the spoken word, and used them rather conservatively." Colin Hemer, Acts in the Setting of Hellenistic History, page 426. That Luke relies on preexisting source material for his speech material in Luke strongly suggests that he was among those ancient historians who believed it was his responsibility to portray speeches as accurately as possible.
B.     Luke Uses a Style Similar Accuracy-Minded Ancient Historians
As an educated Greek, Luke was likely aware of the writings of Polybius and Thucydides, and their efforts to accurately transmit speeches. Moreover, a comparison of Luke's style with other ancient writers demonstrates that "Luke's Greek style is in various ways like that of the serious Hellenistic historians, Polybius in particular." Ben Witherington, The Acts of the Apostles, page 43. Moreover, "[t]his is important because style was an important indicator of how a work should be evaluated in antiquity. Luke's style suggests that he wishes to be heard as a serious Hellenistic historian would be heard, like a Polybius." Ibid.
Of all the historians writing in Greek, Luke's work seem to  be most like the Greek historiography of someone like Polybius, and, to a lesser degree, Thucydides. Indeed, a reasonable case can be made that in terms of method, style, and type of historiography Luke is following this particular Greek tradition of history writing, with some signs of influence Ephorus as well.
Witherington, op. cit., page 33-34.
At the very least, therefore, Luke was aware of and shows an interest in following the example of historians who favored as accurate as possible speech recording. While standing alone these similarities do not show that Luke followed their example, combined with Section A above and Sections C and D below, it is probative evidence that he intended to do so.
C.     Luke's Style of Writing in Acts
Some have objected that the language of the speeches is too Lukan in style to reflect anyone else's words. Moreover, some have argued that the speeches of Peter and Paul are too much alike, and that especially Paul's are too distinct from his letters to reflect a true Pauline source. However, even in the Gospel of Luke, where Luke indisputably relies faithfully on pre-existing sources, Luke polishes the Greek and writes in a consistently Lukan style. Indeed, without the Gospels of Matthew and Mark, it would be difficult to have detected that Luke was using pre-existing sources or determine their boundaries even if we did. Moreover, no one suggests that Luke is providing us with verbatim transcripts of what was said. Accordingly, this objection has little merit.
Furthermore, most of the speeches attributed to Peter and Paul in Acts were directed to pagan or Jewish audiences, whereas the canonical letters that bear their names were directed to Christians. All of the undisputed Paulines were addressed either to churches or to an individual who was already a Christian. Therefore, the audiences were different. The context was different. And the purpose was different. So, we should not expect them to be remarkably similar.
D.     Several Speeches in Acts Are NonLukan and Correspond with External Sources
Despite Luke's quality Greek and the different contexts, he recites four important speeches that demonstrate marks of relying on pre-existing non-Lukan materials.
1.     Stephen's Speech Prior to His Martyrdom
The speech o