the triads of the major scale

Here is a C major scale:

What we're going to do now is build triads on top of each of those scale degrees (except for the 8th scale degree because it's the same as the 1st and will give us the same chord). We will do this by using only notes from the C major scale, that is with no sharps or flats. What we get is the following:

The chord built on C gives us a C major triad, the chord built on D gives us a D minor triad, the one on E gives us E minor, F gives us F major, G gives us G major and A gives us A minor. Lastly the chord built up from B gives us a B diminished triad.

So you might wonder, why the Roman numerals in the chart? These numerals are actually very helpful, because they give us a more general way to talk about the chords in any major scale/key. Since all major keys are built up from the same recipe (a sequence of WWHWWWH steps) all the chords built up from the individual degrees will likewise occur in a predictable pattern.

Put more simply: In D major the chord built on the D (I) gives us a D major triad. In B flat major a chord built on Bb (the I) gives us a Bb major triad. In F sharp major the chord we get on C# is C# major, the V chord, just as we got a G major chord in C major. 

Here's a quick way to think about it:

I, IV, V are Major triads 

II, III, VI are Minor triads

VII is a diminished triad.

This is important information because if you find a chord progression like the following:

Gmaj | Amaj | Cmaj | Dmaj 

You know right away that the entire thing is NOT in one single key. Why? because there are FOUR DIFFERENT major chords, and in any given major key there are only three. 

If on the other hand we had only the following chords:

Gmaj | Cmaj | Dmaj 

we would be dealing with the I, IV and V of G major. 

How about these chords:

Emaj | Dmaj | Amaj

Why is the above key not E major? If it were in E major the VII should be a D# diminished chord, but here we have D major, a bVII with respect to E major. 

Why is it not in the key of D? If the above were in D major the II chord should be E minor, but here we have E major. 

Are all of the above chords found in the key of A major? YES! E major is the V chord, D major is the IV and A is the I. 

For some more practice check out the following post.