The midpoints of a triangle's sides are joined, and a line is drawn from the top vertex straight down to the middle of the base. How many triangles are there in the figure?

Top part: 2 small halves and the whole top triangle, 3. Middle: 2 halves of the upside-down triangle and the whole of it, 3. Bottom corners: 2. Triangles from the top vertex down to the base midpoint, one each side of the median: 2. The two halves of the big triangle and the big triangle itself: 3. Total $3+3+2+2+3=13$.