Geometry · Areas of triangles · Quadrilaterals · Diagonals · Parallelograms · Convexity
Each diagonal of a quadrilateral \(ABCD\) divides it into two parts of equal area. Prove that \(ABCD\) is a parallelogram.
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Serbian Regional Competition (Okruzno takmicenje) 1995, high school grade I, problem 4. The 1995 regional paper was not split into categories. Organized by the Mathematical Society of Serbia (DMS).