Given triangle A0B0C0. On the segment A0B0 points A1, A2, ..., An, and on the segment B0C0 - points C1, C2, ..., Cn so that all segments AiCi+1 (i=0, 1, ...,n−1) are parallel to each other and all segments CiAi+1 (i=0, 1, ...,n−1) are too. Segments C0A1, A1C2, A2C1 and C1A0 bound a certain parallelogram, segments C1A2, A2C3, A3C2 and C2A1 too, etc. Prove that the sum of the areas of all n−1 resulting parallelograms less than half the area of triangle A0B0C0. geometryareasgeometric inequality