Geometry Problem 146: Varignon's Theorem: Quadrilateral, Midpoints, Parallelogram, Area, Perimeter, iPad Apps

Proposition

In the figure below, ABCD is a quadrilateral of area S. E, F, G, and H are the midpoints of the sides. S₁, S₂, S₃, and S₄ are the areas of triangles AEH, BEF, CFG, and DGH respectively. Prove that: (1) EFGH is a parallelogram, called Varignon parallelogram, (2) the perimeter of the Varignon parallelogram is equal to the sum of diagonals of ABCD, (3) S₁+ S₃ = S₂ + S₄ = S / 4, (4) the area of the Varignon parallelogram is half that of ABCD.

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Geometric Art using Mobile Apps

Geometric art is a form of art based on the use and application of geometric figures. A geometric figure is any set or combination of points, lines, surfaces and solids.

A mobile app or mobile application software is a computer program designed to run on smartphones and tablet computers.

See also:
Original problem 146.