Take any triangle. Label it ABC. Construct D and E as the midpoints of BC and AB, respectively. Now construct DF and EF, where F is any point on AC. Now look at the triangles AEF and FCD and the quadrilateral BEFD. How are the areas of the triangles related to the area of the quadrilateral? What happens as F moves along AC? Can you explain why you think you're right?Please prove your answer - provide an explanation that can't be argued with!
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