Let's go through our major CAGED systems and see how we can trim each chords down to just the 1st, 3rd, and 5th. Let's start with C major, and we're going to start with the C shape. Remember, it's 1-3-5-1-3. So if we omit the final 1-3 and we have one trimmed-down triad.

C Shape

You can see that there's more trimmed-down triads in this shape if we allow inversions, i.e 3-5-1. But right now, let's focus on 1-3-5, and the name for this type of triad the root position.

A Shape

G Shape

E Shape

D Shape

Looking at the D shape, there's no direct root position shapes (1-3-5), so this shape is omitted.