In music theory, the "family" of chords for a key is typically the set of diatonic chords—chords built from the notes of the scale by stacking thirds (every other note). For D minor, we assign Roman numerals to each chord based on its position in the scale:
i: D minor (Dm) - D, F, A
(Root chord, the tonic, built on D)
ii°: E diminished (Edim) - E, G, Bb
(Diminished chord, built on E)
III: F major (F) - F, A, C
(Relative major, built on F)
iv: G minor (Gm) - G, Bb, D
(Subdominant minor, built on G)
v: A minor (Am) - A, C, E
(Minor chord, built on A; note that in natural minor, this is minor, not major unless altered—see harmonic minor below)
VI: Bb major (Bb) - Bb, D, F
(Built on Bb, a bright-sounding chord in this key)
VII: C major (C) - C, E, G
(Built on C, often leads back to Dm)