Three lines are drawn in an equilateral triangle, each parallel to a side and one-third of the way across, as shown. How many triangles are there?

Small triangles with sides one-third of the big side: 3. Medium triangles with sides two-thirds of it (each made by one of the new lines with two sides of the big triangle): 3. The whole triangle: 1. Total $3+3+1=7$.