If you have a C major triad with a root, 3rd and 5th in the key of C major, would a G major triad still be composed of a root, 3rd and a 5th?
Yes, the G major triad would be root, major 3rd and perfect 5th. This isn't only for the major triad; it works the same way in the minor, augmented and the diminished ones. You just change the formula. Most of the common chords used in Western music are built on thirds. So, if you are in the C major scales, you can have 7 chords:
- C major: root, maj third, fifth
- D minor: root, min third, fifth
- E minor: root, min third, fifth
- F major: root, maj third, fifth
- G major: root, maj third, fifth
- A minor: root, min third, fifth
- B diminished: root, min third, diminished fifth
This really depends on which root, third and fifth we are talking about.
Rule: a triad consists of a root, third and fifth - the (as yet unqualified, because that will depend on the type of triad) third and fifth being relative to the root note. These are the chord tones.
A major triad will consist of the root, a major third and a perfect fifth (again, intervals measured from the root note).
When considering chords in a key, we will be looking at the scale tones, or degrees that are used to make up the chord. Thus, in C, the C major chord will be composed of the first, third and fifth degree (tone) of the C major scale.
What about G major? Assuming we're still in C, its root note is the fifth degree of the C major scale (G), its third is the seventh degree (B) and its fifth is the ninth/second degree (D). If we were in G, then the chord tone/scale tone correspondence would be the same as for C major in C.
In other words, there is a bit of an ambiguity of terminology, when we use words like third or fifth with regards to chords in a key.