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Two Midpoints of a Trapezoid

Let ABC be a triangle. Let D be a point on AB and DE be parallel to AC with E on BC. Let AE and DC intersect at F. Let BF intersect DE at N and AC at M. Then DN = NE and AM = MC.

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The statement of the theorem is in Trapezoid: Triangle, Diagonals, Midpoints, Bases.

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"Two Midpoints of a Trapezoid" from the Wolfram Demonstrations Project
 http://demonstrations.wolfram.com/TwoMidpointsOfATrapezoid/
Contributed by: Jay Warendorff
After work by: Antonio Gutierrez
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