In δabc shown below, point a is at (0, 0), point b is at (x2, 0), point c is at (x1, y1), point d is at
(x sub 1/2 , y sub 1/2) and point e is at
( x sub 1+ x sub 2 /2, y sub 1 /2)

prove that segment de is parallel to segment ab.

You can prove that triangles abc and edc are congruent using a sas argument. then see which angles of triangle abc correspond to angles of triangle edc, and try to argue that ab and de are parallel.

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