This is what’s called the Synoptic Problem, and it’s a “problem” because, while what you say is accurate, there is no clear proof of the conclusions reached.
Briefly, here’s what the evidence is:
A. About 95% of Mark’s Gospel duplicates about two-thirds of Matthew’s, including large chunks of text either verbatim identical or “variant by pattern” (e.g., “Kingdom of God” in one is always “Kingdom of Heaven” in the other, and otherwise a near-verbatim match).
B. Large portions of Luke match the Matthew-Mark equivalences.
C. The differences are largely, but not exclusively, in: (1) Each Gospel has a somewhat different Crucifixion-Resurrection account; (2) Matthew and Luke add Infancy narratives and genealogies at the beginning; (3) Matthew and Luke each add large amounts of Jesus’s teaching to what Mark records.
D. Something over half of the teachings in Matthew and Luke are duplicative of each other, going well beyond what duplicates Mark.
E. Where Jesus is alleged to have given a teaching often does not match between Gospels, particularly in the material common to Matthew and Luke but not Mark.
F. The early Christian historian Eusebius quotes the even earlier writer Papias as claiming that "Matthew wrote the logia of Jesus first, in the Hebrew language.
G. This does not match Matthew’s Gospel as we have it, which (1) gives every sign of having been written in Greek, as opposed to being a translation; (2) shows clear signs of having borrowed heavily from Mark and another text; (3) is not a logia document (as the non-canonical Gospel of Thomas is – i.e., a collection of short teachings, not put in any context) but a life-and-teachings narrative.
H. What Luke has spread throughout his narrative about teachings is largely concentrated in Matthew in five long topical teachings, of which the Sermon on the Mount and the Eschatological Discourse are typical.
Most scholars are convinced that Mark was written before the other two, and that they were compiled by editors using Mark and a hypothetical document tagged “Q” (for German quelle, “source”). Matthew and Luke used Mark as “frame story,” inserting teachings material from Q in different locations (Matthew almost certainly topically, Luke quite probably as accurate in terms of setting as its author could get). A significant minority of Bible scholars, including myself, are convinced that what Papias spoke of as written by Matthew is actually what we reference as “Q.”
The traditional attributions of the existing Gospels are the subject of skeptical questioning, as there is no proof they were written by the men they are attributed to, and some circumstantial evidence that suggests they were not.