The three-sliced triangle
A general triangle has its three edges each divided into three equal sections. You label all these points (the corners and the marks on the edge) 1,2,3,1,2,3,1,2,3 starting at one of the corners. Then you draw lines to join each of the 1's to the 2 on the opposite edge. Now there is a little triangle in the centre. How many times bigger than the small triangle is the big triangle? Move the points marked "1" to see what happens to the areas of the two triangles and their ratio. Can you prove why this works?