Virgo belongs to the element of Earth and moves through life in the Mutable mode, ruled by Mercury. Sagittarius belongs to the element of Fire and moves in the Mutable mode, ruled by Jupiter.
Fire wants to move fast; earth wants to move surely. This is the most common source of friction in fire–earth pairings, and it is also where the growth lives. One partner teaches momentum, the other teaches patience.
Both of you adapt. The upside is flexibility and easy play; the downside is that important decisions can drift if neither of you plants the stake. Sometimes it helps to hold ground on purpose.
One sign is active, the other receptive — the classic complementary polarity that most astrological literature treats as a natural fit. One of you leads the outward motion, the other holds the inner world.
What follows is a general read on this pair. Real compatibility depends on the whole natal chart — use the calculator linked on this page to compare two full charts when you're ready.