An upside-down triangle joins the midpoints of a triangle's sides, and a horizontal line crosses the figure through the middle of the inner triangle. How many triangles are there?

The horizontal line cuts the bottom tip off the inner triangle and cuts off the tops of the two lower corner triangles: 3 small. Then the 3 corner triangles and the inner triangle, 4. The big triangle above the horizontal line, 1, and the whole, 1. Total $3+4+1+1=9$.