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another proof 1) draw 3 additional lines parallel to each cevian passing through the remaining vertices of 2 triangles. 2) show that 6 other shaded triangles are mirror images of the green triangle and therefore have the same area 3) show that every part of a shaded triangle that lies outside of the big triangle has an equal unshaded part inside the big triangle. Midpoints of big triangle's sides are points of symmetry.
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