In the figure below, given a
quadrilateral ABCD, M and N are the midpoints of AC and BD
respectively. If S, S_{1}, S_{2}, and S_{3}
are the areas of the quadrilaterals ABCD,BCNA, BCDM, and BCNM
respectively, prove that: \(S_1 = S_2 = \dfrac{S}{2} = 2\cdot S_3\).
HINTS:
1. AREA OF A TRIANGLE:
Median Area Fact:
A median divides the triangle into
two triangles of equal area.
Geometric Art: Hyperbolic Kaleidoscope of problem 87
using iPad Apps.
Geometric Art using Mobile Apps
A mobile app or mobile application software is a computer program designed to run on smartphones and tablet computers.
Hyperbolic Kaleidoscope, Poincare Disk Model
Poincare disk model is a model of 2dimensional hyperbolic geometry in which the points of the geometry are inside the unit disk, and the straight lines consist of all segments of circles contained within that disk that are orthogonal to the boundary of the disk, plus all diameters of the disk.
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Tessellation
A tessellation of a flat
surface is the tiling of a plane using one or more
geometric shapes, called tiles, with no overlaps and
no gaps.
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Kaleidoscope
A continually changing symmetrical pattern of shapes and colors.
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