Geometry · Convex hexagon · Area bisection · Areas with a common base · Trapezoid · Parallel lines
Problem 1, 1999
In a convex hexagon \(ABCDEF\), each of the two diagonals \(AD\) and \(BE\) divides the hexagon into two pieces of equal area. Prove that the quadrilateral \(BDEA\) is a trapezoid.
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Serbian Republic Competition (Republicko takmicenje) 1999, high school grade I, category A, problem 1. Organized by the Mathematical Society of Serbia (DMS). Source