I'm afraid I don't understand what you are trying to tell me.
You already know your triads are Root, 3rd, 5th.
You may see that chords can be made by "stacking thirds"
aka "skipping every other note" from the root:
R 2 3 4 5 the little numbers are tones we skip over
You can extend that beyond the 5th to build
7th chords
R 2 3 4 5 6 7
And if you play jazz ( or are similarly mentally unstable ) you can keep going,
past the octave, into
extensions
R 2 3 4 5 6 7 ... 8 9 10 11 12 13
The thing about extensions is: there's only 7 notes in a scale.
By extending on to 9 11 13, we are actually jumping up an octave
and playing notes we "skipped" in the lower octave
... 8 9 10 11 12 13
... R 2 3 4 5 6
9th = 2nd, one octave higher
11th = 4th, one octave higher
13th= 6th, one octave higher
so the "chord" C major 7 9 11 13 actually would contain
all the notes of a c major scale.
It will also sound like @ss unless carefully voiced.
If you got all that, then finally: Since the chunk
9 11 13 are enharmonic with
2 4 6
It actually represents a triad whose root is the 9th(2nd) in previous chord.
Thus C maj 7 9 11 13 = triads C maj + D min
Isn't math fun?
--
Ultimately I wouldn't worry too much about it.
You asked about triads, and jackasses like me
are throwing 7th chords and extensions at you,
which you can tackle later,
after you sort out the triads.