Online Geometry Problem 151: Quadrilateral, Area, Trisection of Sides. Level: High School, Honors Geometry, College, Mathematics Education

In the figure below, ABCD is a quadrilateral of area S. E, F, G, H, M, N, P, and Q trisect the sides. If S₁, S₂, S₃, and S₄ are the areas of the shaded quadrilaterals, prove that: S₁ + S₃, = S₂ + S₄. View or post a solution
 

See also:
Geometric Art: Hyperbolic kaleidoscope